Eighty-four pollen samples were obtained for 80 taxa, of which, 13 species and one variety are from sect. Brachycalyx Sweet, 58 species and two varieties from sect. Tsutsusi Sweet, and six species from subgen. Pentant...Eighty-four pollen samples were obtained for 80 taxa, of which, 13 species and one variety are from sect. Brachycalyx Sweet, 58 species and two varieties from sect. Tsutsusi Sweet, and six species from subgen. Pentanthera （G. Don） Pojarkova, respectively. Pollen morphology of all samples was observed using LM and SEM. Pollen grains are revealed to be spheroidal and tetrahedral with tricolporate apertures. Pollen sizes of subgen. Tsutsusi （Sweet） Pojarkova range from 37.67 μm to 61.06μm, and the exine sculptures are more or less compactly granulated. Pollen sizes are significantly different between sect. Brachycalyx and sect. Tsutsusi of subgen. Tsutsusi. Rhododendron tashiroi Maxim. of sect. Tsusiopsis Sleumer shows a close affinity to sect. Brachycalyx. Pollen size and exine are consistent with general morphology in differentiating species in sect. Tsutsusi. Rhododendron huadingense B. Y. Ding ＆ Y. Y. Fang, once placed as a member of sect. Brachycalyx, should be considered as a species in subgen. Pentanthera.展开更多
A REDUCE code for the Newman-Janis algorithm is described. This algorithm is intended to include rotation into nonrotating solutions of the Einstein field equations with spherically symmetry or perturbed spherically s...A REDUCE code for the Newman-Janis algorithm is described. This algorithm is intended to include rotation into nonrotating solutions of the Einstein field equations with spherically symmetry or perturbed spherically symmetry and has been successfully applied to many spacetimes. The applicability of the code is restricted to metrics containing potentials of the form 1/r.展开更多
A new approach was proposed for grouping separation of 14 lanthanide rare-earth ions from their coexisting mixed aqueous solutions, by performing liquid-column elution using the aqueous solution containing 14 lanthani...A new approach was proposed for grouping separation of 14 lanthanide rare-earth ions from their coexisting mixed aqueous solutions, by performing liquid-column elution using the aqueous solution containing 14 lanthanide rare-earth ions as the stationary phase and the dispersed organic oil droplets containing P507 extractant as the mobile phase. It was revealed that 14 lanthanide rare-earth ions could be separated into four groups, according to the lanthanide tetrad effect, respectively eluting out from the liquid column at different time in a certain order. Various effects including the saponification degree of P507, the concentration of P507 in organic phase, the length and inner diameter of the extraction column on the performance of grouping separation of rare-earth ions were discussed. The changes of the mass transfer coefficients were also investigated. The separation efficiency of the four groups of rareearth elements(REEs) was evaluated based on the elution resolution, Rs, of the elution peaks of La(Ⅲ),Gd(Ⅲ), Ho(Ⅲ) and Lu(Ⅲ), the four representative elements respectively from each of the four groups of REEs. Experimental results demonstrated that the separation of REEs by liquid-column elution mainly depended on the competitive adsorption of different rare-earth groups onto the surface of ascending P507 oil droplets. The affinity of different rare-earth groups with P507 extractant and a limited adsorption capacity of P507 molecules at the surface of the oil droplets ascending in liquid column play the important role. The present work highlights a promising technique for grouping separation of multiple lanthanide elements co-existing complex systems.展开更多
Fractionations of rare earth elements (REEs) and the forming mechanisms in plants were studied using Triticum aestivum as plant material with application of exogenous REEs and hydroponic culture. REEs were significant...Fractionations of rare earth elements (REEs) and the forming mechanisms in plants were studied using Triticum aestivum as plant material with application of exogenous REEs and hydroponic culture. REEs were significantly fractionated in different parts of Triticum aestivum. M-type tetrad effect could be observed in both root and shoot of Triticum aestivum, which might result from the different abilities of REEs to form phosphate precipitation. Middle REEs (MREEs), light REEs (LREEs) and heavy REEs (HREEs) were enriched in root, stem and leaf of Triticum aestivum, respectively. REE speciation calculations using VMINTEQ program show REEs in simulated xylem solution mainly exist as REE-EDTA^(- )and RE^(3+), but only HREEs are enriched in REE-EDTA^(-), while LREEs are enriched in the other REE species. It is suggested that the fractionation between LREEs and HREEs might be caused by the uptake of REE-EDTA^(-) in Triticum aestivum leaves, but might result from the uptake of the other REE species in their stems.展开更多
Intrusion of quartz-monzodioritic igneous bodies of Oligocene age into Eocene lithic crystal tufts and trachy-basalts resulted in the occurrence of a widespread argillic alteration zone in the Jizvan district （northe...Intrusion of quartz-monzodioritic igneous bodies of Oligocene age into Eocene lithic crystal tufts and trachy-basalts resulted in the occurrence of a widespread argillic alteration zone in the Jizvan district （northern Iran）. Mineralogically, the argillie alteration zone includes minerals such as kaolinite, quartz, smectite, pyrophyllite, muscovite-illite, alunite, rutile, calcite, feldspar, chlorite, hematite and goethite. Therefore, the non-CHARAC behaviour for trace elements in the argillic samples is reflected in the non-chondritic Y/Ho and Zr/Hf ratios and the irregular REE patterns, which appear related to the tetrad effect phenomenon. The chondrite-normalized REE distribution patterns indicate both concave （W-shaped） and convex （M-shaped） tetrad effects in the argillic samples. Based on the field evidence and the results from geochemical studies, it can be concluded that the samples from the argillic alteration zone having high fourth tetrad effect values （〉0.30） were developed in the fault and breccia zones. The results indicate that factors such as preferential scavenging by Mn-oxides, crystallization of clay minerals, fluid-rock interaction, overprint of hypogene mineral assemblage by supergene ones, and the structural control, have all played an important role in the occurrence of tetrad effects in samples of the argillic zone in the Jizvan district.展开更多
Walegen Au deposit is closely correlated with granitic intrusions of Triassic age, which are composed of granite and quartz porphyries. Both granite porphyry and quartz porphyry consist of quartz, feldspar and muscovi...Walegen Au deposit is closely correlated with granitic intrusions of Triassic age, which are composed of granite and quartz porphyries. Both granite porphyry and quartz porphyry consist of quartz, feldspar and muscovite as primary minerals. WeaMy peraluminous granite porphyry （A/ CNK=1.10-1.15） is enriched in LREE, depleted in HREE with Nb-Ta-Ti anomalies, and displays subduction-related geochemistry. Quartz porphyry is strongly peraluminous （A/CNK=1.64-2.81） with highly evolved components, characterized by lower TiO2, REE contents, Mg#, K/Rb, Nb/Ta, Zr/Hf ratios and higher Rb/Sr ratios than the granite porphyry. REE patterns of quartz porphyry exhibit lanthanide tetrad effect, resulting from mineral fractionation or participation of fluids with enriched F and CI. LA- ICP-MS zircon U-Pb dating indicates quartz porphyry formed at 233±3 Ma. The ages of relict zircons from Triassic magmatic rocks match well with the detrital zircons from regional area. In addition, εHf（t） values of Triassic magmatic zircons from the granite and quartz porphyries are -14.2 to -9.1 （with an exception of ＋4.1） and -10.8 to -8.6 respectively, indicating a crustal-dominant source. Regionally, numerous Middle Triassic granitoids were previously reported to be formed under the consumption of Paleotethyan Ocean. These facts indicate that the granitic porphyries from Walegen Au deposit may have been formed in the processes of the closing of Paleotethyan Ocean, which could correlate with the arc-related magmatism in the Kunlun orogen to the west and the Qinling orogen to the east.展开更多
The Guidong granitic complex is constituted by Luxi pluton, Xiazhuang pluton, Maofeng pluton, Sundong pluton, Aizi pluton and Siqian pluton, which intruded in Indosinian and early Yanshanian Periods. These plutons var...The Guidong granitic complex is constituted by Luxi pluton, Xiazhuang pluton, Maofeng pluton, Sundong pluton, Aizi pluton and Siqian pluton, which intruded in Indosinian and early Yanshanian Periods. These plutons varies from each other not only in major element content, aluminium saturation index, but also in ∑REE, δEu, and LREE/HREE, （La/Yb）N, （La/Sm） N and （Gd/Yb） N ratios. Uranium mineralization is mainly hosted by strong peraluminous granites, which has undergone intense fluid-rock interaction, and their REE compositions are characterised by M-type tetrad effects and lower ∑REE, δEu value, LREE/HREE, （La/Yb） N, （La/Sm） N and （Gd/Yb） N ratios.展开更多
The Hizeh-Jan kaolin deposit(northwest of Varzeghan, East-Azarbaidjan Province, NW Iran) is a product of the alteration of Eocene andesitic rocks. Based on mineralogical examinations, kaolinite, quartz, smectite, pyro...The Hizeh-Jan kaolin deposit(northwest of Varzeghan, East-Azarbaidjan Province, NW Iran) is a product of the alteration of Eocene andesitic rocks. Based on mineralogical examinations, kaolinite, quartz, smectite, pyrophyllite, muscovite-illite, alunite, calcite, diaspore, goethite and hematite are the most abundant mineral phases in this deposit. The geochemical indicators, such as Y/Ho and Zr/Hf, indicate the non-CHARAC(non-Charge-radius control) behavior of these pairs, which are likely to be due to the occurrence of the tetrad effect phenomenon in this deposit. Simultaneous concave and convex shapes in the chondrite-normalized REE distribution patterns are a remarkable feature of the kaolin samples. Bivariate diagrams of the size of the third tetrad effect(T_3) versus geochemical parameters such as Y/Ho, Nb/Ta and Zr/Hf ratios display two distinct populations for the kaolin samples. The first population is characterized by high T_3 values(>0.13), which are near or on the fault zone. The second population is characterized by low T_3 values(<0.13), and are farther from the fault zone. The obtained results from the geochemical data have furnished compelling evidence that fluidrock interaction, overprint of hypogene processes by supergene ones, and structural control, are key controlling factors for the occurrence of tetrad effects in REE distribution patterns in the Hizeh-Jan kaolin deposit.展开更多
Study of the concentration of major,trace,and rare earth elements(REE)in the Shahindezh karst bauxite deposit,northwestern Iran clarifies the relationship of the tetrad effect with geochemical parameters in the bauxit...Study of the concentration of major,trace,and rare earth elements(REE)in the Shahindezh karst bauxite deposit,northwestern Iran clarifies the relationship of the tetrad effect with geochemical parameters in the bauxite ores.The existence of irregular curves in the chondrite-normalized REE patterns as well as non-CHARAC behavior of geochemically isovalent pairs(Y/Ho)are related to the tetrad effect.The meaningful positive correlation between the sizes of the calculated T3 tetrad effect and some geochemical factors such as Y/Ho,ΣREE,La/Y,(La/Yb)N,and(LREE/HREE)N as well as some major oxides-based parameters like Al2O3+LOI/SiO2+Fe2O3,Al2O3/Fe2O3,Al2O3+LOI,IOL,and SiO2+Fe2O3indicate that the studied bauxite horizon was likely deposited by different(acidic and/or alkalic)solutions at different stages.The lower part of the studied horizon with a thickness of^4.7 m displays alkali characteristics whereas the upper parts of the horizon with a thickness of^5.3 m are characterized by more acidic conditions.These results are fully supported by the co-occurrence of convex-concave tetrad effect curves in the chondrite-normalized REE patterns.Therefore,the tetrad effect phenomenon used in this study has proved to be a good and reliable geochemical proxy to assess the conditions of the depositional environment in the Shahindezh bauxite ores.展开更多
Paleozoic rocks in the Wadi El Sahu area are affected by many major faults in different directions.A reverse fault trending NE-SW is exposed for about 300 m of its length as it cuts through the Abu Hamata and Adedia f...Paleozoic rocks in the Wadi El Sahu area are affected by many major faults in different directions.A reverse fault trending NE-SW is exposed for about 300 m of its length as it cuts through the Abu Hamata and Adedia formations on the south side of Wadi El Sahu.A secondary ascending hydrothermal solution carrying heavy metals and radioactive minerals passed through the fault plain and the surrounding fractures,forming mineralized and radioactive zone.The mineralized zone thickness ranges from 60 cm to 200 cm along the fault plain.These rocks were analyzed radiometrically using a portable gamma-ray spectrometer,chemically by employing ICP-ES and ICP-MS,as well as mineralogically by both binocular and Environmental Scanning Electron microscope.Gold content was also determined by fire assay.REE and U contents reached up to 2682 and 1216 ppm,respectively.Mineralogical investigations indicated the presence of uraninite,torbernite,autunite,sklodowskite,kasolite as uranium minerals,thorite as a thorium mineral,monazite,allanite and xenotime as REE-bearing minerals,zircon and columbite as accessory minerals,gold and nickel as precious and base metals,in addition to cassiterite,chalcopyrite,chalcocite and chrysocolla.High REE and U contents are attributed to the circulation of epigenetic U and REE-bearing hydrothermal solutions along the fault plain and its surrounding fractures.Hydrothermal alteration processes could then be confirmed by the presence of the M-type tetrad effect in the REE-patterns of the ferruginous sandstone.The non-chondritic ratio of Nb/Ta,Zr/Hf and Y/Ho in the studied sandstone may be attributed to the tetrad effect.The Ce and Eu anomaly with unusual REE-patterns was represented by the presence of conjugated M-W tetrad effects,indicating either the dual effect of hydrothermal solutions or groundwater with seawater.The results clarify that the tetrad-effects could be used as evidence for the environment of deposition and as an indication for gold mineralization.展开更多
The Abu Dabbab albite granite(ADAG),in the central Eastern Desert of Egypt,hosts the most significant rare metal ore deposit in the northern part of the Neoproterozoic Arabian-Nubian Shield.Here,we report detailed fie...The Abu Dabbab albite granite(ADAG),in the central Eastern Desert of Egypt,hosts the most significant rare metal ore deposit in the northern part of the Neoproterozoic Arabian-Nubian Shield.Here,we report detailed field,petrographic,mineralogical and geochemical investigation of the ADAG,an isolated stock-like granitic body with sharp intrusive contacts against metamorphic country rocks,probably emplaced at about 600 Ma.The fine-grained porphyritic upper unit is a preserved remnant of the shallowly-emplaced apex of the magma chamber,whereas the medium-grained lower unit crystallized at deeper levels under subvolcanic conditions.The peraluminous leucocratic ADAG shares common geochemical characteristics with post-collisional intraplate A-type magmas.In addition to the conspicuous enrichment in Na2O,the ADAG is remarkable for its anomalous concentrations of Ta,Nb,Li,Hf,Ga,Sn,Zn and heavy rare-earth elements.Nb-Ta minerals in the ADAG are mixed with Fe-Mn oxides,forming black patches that increase in abundance toward of the base of the intrusion.Columbite-tantalite,cassiterite and wolframite are the most important ore minerals.Pronounced negative Eu anomalies(Eu/Eu*=0.10–0.24)reflect extreme magmatic fractionation and perhaps the effects of late fluid-rock interaction.The ADAG was most likely generated by partial melting of the juvenile middle crust of the ANS as the geotherm was elevated by erosional uplift following lithospheric delamination and it was emplaced at the intersection of lineations of structural weakness.Although formation of the ADAG and its primary enrichment in rare metals are essentially due to magmatic processes,late-stage metasomatism caused limited redistribution of rare metals.Fluid-driven subsolidus modification was limited to the apex of the magma chamber and drove development of greisen,amazonite,and quartz veins along fracture systems.展开更多
The deep understanding of 4f-correlated electron motion behavior is experimentally limited due to similar physicochemical properties of rare earth elements(REEs).While the solvent extraction behavior originating from ...The deep understanding of 4f-correlated electron motion behavior is experimentally limited due to similar physicochemical properties of rare earth elements(REEs).While the solvent extraction behavior originating from the continuous occupation of 4f electrons along the lanthanide family provides a particular platform to probe the 4f electrons motion behavior and its correlations to their versatile functions.Herein,the complexation between REEs and the prototypical extractant of diethyl phosphoric acid(DEP)was substantially studied based on quantum mechanical calculation.The results firstly show that the average bond lengths between Ln and six coordinated oxygen atoms are consistent with lanthanide contraction phenomenon,and gadolinium break effect is also obviously observed.Secondly,the"tetrad effect"is figured out based on the subtle discrepancy of 4f electrons occupation,namely La-Nd,Sm-Eu,Gd-Dy and Ho-Lu.Specifically,the main composition is 4f5d6p for La-Nd,while the discrepancy is due to the increasing electrons in the 5d shell,while it is 4f5d for Pm-Eu.For Gd-Dy,their 4f orbitals accept little electrons and the donating electrons flow into 6s5d subshells due to the half-filled stability and the enhancement of shielding effect.The electrons donate into 5d6p subshells due to multiply electrons occupation of 4f orbitals for Ho-Lu.These detailed analyses obviously clarify the"tetrad effect"along the lanthanide family due to the different variation of 4f orbital occupation.It is expected that these microscopic understandings provide important guidance for the separation of REEs and the design of new extractants.展开更多
The widespread W-(Mo)-Sn-Nb-Ta polymetallic mineralization in Southeast(SE)China is genetically associated with Mesozoic highly fractionated granitic rocks.Such rocks have enigmatic mineralogical and geochemical featu...The widespread W-(Mo)-Sn-Nb-Ta polymetallic mineralization in Southeast(SE)China is genetically associated with Mesozoic highly fractionated granitic rocks.Such rocks have enigmatic mineralogical and geochemical features,making its petrogenesis an intensely debated topic.To better understand the underlying magma evolution processes,petrography,garnet chemistry and whole-rock major and trace element data are reported for Jurassic highly fractionated granitic rocks and associated microgranite and aplitepegmatite dikes from Macao and compared with coeval similar granitic rocks from nearby areas in SE China.Despite the fact that the most evolved rocks in Macao are garnet-bearing aplite-pegmatite dikes,the existence of coeval two-mica and garnet-bearing biotite and muscovite granites displaying more evolved compositions(e.g.,lower Zr/Hf ratios)indicates that the differentiation sequence reached higher degrees of fractionation at a regional scale.Although crystal fractionation played an important role,late-stage fluid/melt interactions,involving F-rich fluids,imparted specific geochemical characteristics to Macao and SE China highly fractionated granitic rocks such as the non-CHARAC(CHArge-and-RAdius-Controlled)behavior of trace elements,leading,for example,to non-chondritic Zr/Hf ratios,Rare Earth Elements(REE)tetrad effects and Nb-Ta enrichment and fractionation.Such process contributed to the late-stage crystallization of accessory phases only found in these highly evolved facies.Among the latter,two populations of garnet were identified in MGI(Macao GroupⅠ)highly fractionated granitic rocks:small grossular-poor euhedral grains and large grossular-rich skeletal garnet grains with quartz inclusions.The first group was mainly formed through precipitation from highly evolved Mn-rich slightly peraluminous melts under low-pressure and relatively low temperature(~700℃)conditions.Assimilation of upper crust metasedimentary materials may have contributed as a source of Mn and Al to the formation of garnet.The second group has a metasomatic origin related to the interaction of magmatic fluids with previously crystallized mineral phases and,possibly,with assimilated metasedimentary enclaves or surrounding metasedimentary strata.The highly fractionated granitic rocks in Macao represent the first stage in the development of granite-related W-(Mo)-Sn-Nb-Ta mineralization associated with coeval more evolved lithotypes in SE China.展开更多
The muscovite granites at the study area are being emplaced into biotite granites and ophiolitic mélange settings. They occur in four exposures namely;Umm Seleimat, Sikait, Umm El Kheran and Umm Addebaa exposure....The muscovite granites at the study area are being emplaced into biotite granites and ophiolitic mélange settings. They occur in four exposures namely;Umm Seleimat, Sikait, Umm El Kheran and Umm Addebaa exposure. The presence of garnet and muscovite flakes may reflect the peraluminous nature of the studied muscovite granites. Petrographically, the studied granites are mostly subsolvus and consist of plagioclase, K-feldspars, quartz, muscovite and biotite. Garnet, zircon, allanite and opaques are accessories. The textural features of these granites are expressed by bent plagioclase lamellae, distorted microcline twinning, deformed mica flakes and development of myrmekite and recrystallization of feldspars into fine-grained aggregates. Umm Seleimat and Sikait exposures are more differentiated due to the presence of high content of K-feldspar and LREEs. The REE budget decreased from Umm Seleimat-Sikait exposures to Umm El Kheran-Umm Addebaa exposures as (514.5 - 495.6) to (195.9 - 197.7), respectively. Umm Seleimat-Sikait exposures have lower HREE/LREE (0.12 - 0.67), relative to Umm El Kheran-Umm Addebaa exposures (0.99 - 2.06). The studied granites revealed that the chondrite normalized REE patterns are the normal M-type of tetrad effect, where TE1,3 tetrad effect is higher than 1 in all samples which implies that there was an interaction between melt and water-haloid-rich fluid when these granites are crystallized from magma. Spectrometric values of Umm Seleimat and Umm Addebaa indicate that U content is more than Th content. Applying the U mobilization equation proved that the studied granites have been originated from a late magmatic phase of magma very rich in radioelements, also the majority of measurements lie above the zero line indicating that the studied granites affected with hydrothermal solutions rich in uranium than thorium which indicates uranium addition.展开更多
The energy-momentum distributions of Einstein＇s simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann-Thomson, Landau-Lifshitz （LL）, Moller ...The energy-momentum distributions of Einstein＇s simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann-Thomson, Landau-Lifshitz （LL）, Moller and Papapetrou energy-momentum complexes are used in general relativity. While Einstein and Bergmann-Thomson complexes give exactly the same results, LL and Papapetrou energy-momentum complexes do not provide the same energy densities. The Moller energy-momentum density is found to be zero everywhere in Einstein＇s universe. Also, several spacetimes are the limiting cases considered here.展开更多
PAMAM/lanthanide （Ⅲ） nanocomposite was studied by molecular simulation method. Molecular simulation enabled study of the lanthanide tetrad effect at atomic level. However, PAMAM dendrimer exhibiting unique properti...PAMAM/lanthanide （Ⅲ） nanocomposite was studied by molecular simulation method. Molecular simulation enabled study of the lanthanide tetrad effect at atomic level. However, PAMAM dendrimer exhibiting unique properties such as nanometer size and highly functionalized terminal surface provided a novel space for lanthanide （Ⅲ） to show their peculiar tetrad effect. The results showed that total energies of PAMAM/lanthanide（Ⅲ） nanocomposites presented obvious tetrad effect and special double-double effect. Nd, Gd, and Er fell to the lower point and Gd fell to the lowest point in the TE-Ln curve with four groups. In order to explain the tetrad effect, kinetic energy （KE） and potential energy （PE） were analyzed. The KE curve consisted of three W-type parts （La - Pm, Pm - Tb, Tb - Tm, and the latter two W-type part were axial symmetry） and an exception part （Yb - Lu）. It also showed that the KE of odd atomic number was higher than the even one＇s with exception of Yb and Lu. Furthermore, decomposed potential energies gave out the atomic-level subtle difference of lanthanide which present more regulations for Eu（Ⅲ） - Lu（Ⅲ） compared with La（Ⅲ） - Sm（Ⅲ）. And also Ho-valley and three platforms （Sm - Eu, Td - Dy, Er - Tm） were discovered that refect the regular change of nanocomposite structures. Additionally, there are distinct correlations between Ebond and EInversion, EAngle and EVDW, Eworsion and ECoul, respectively. Therefore, PAMAM could be used in separation of lanthanide by changing conditions.展开更多
Guidong granitic complex is constituted by Luxi intrusion, Xiazhuang intrusion, Maofeng intrusion, Sundong intrusion, Aizi intrusion and Siqian intrusion, which emplaced in Indosinian and early Yanshanian Periods. The...Guidong granitic complex is constituted by Luxi intrusion, Xiazhuang intrusion, Maofeng intrusion, Sundong intrusion, Aizi intrusion and Siqian intrusion, which emplaced in Indosinian and early Yanshanian Periods. These intrusions varied from each other not only in major element content, aluminium saturation index, but also in values of ∑REE, δEu, and LREE/HREE, (La/Yb)N, (La/Sm)N and (Gd/Yb)N. The Maofeng intrusion, which has the closest relationship with uranium mineralization, belongs to strong peraluminous granites. Having undergone much intense fluid-rock interaction, it is characterized by typical M-type tetrad effects and lowest values of ∑REE, δEu, LREE/HREE, (La/Yb)N, (La/Sm)N and (Gd/Yb)N ratios than other studied intrusions.展开更多
In the framework of parallelism general relativity, the torsion axial-vector in the rotating gravitational field is studied in terms of the alternative Kerr tetrad. In thecase of the weak field and slow rotation appro...In the framework of parallelism general relativity, the torsion axial-vector in the rotating gravitational field is studied in terms of the alternative Kerr tetrad. In thecase of the weak field and slow rotation approximation, we obtain that the torsion axial-vector possesses the dipole-like structure. Furthermore, the effect of massive neutrino spin precession in this field is mentioned.展开更多
Based on the vector graviton metric theory of gravitation (VGM) suggested by one of the authors of this article, using the method of null tetrad and analytic continuation, this paper gives the metric of the rotating c...Based on the vector graviton metric theory of gravitation (VGM) suggested by one of the authors of this article, using the method of null tetrad and analytic continuation, this paper gives the metric of the rotating charged spherical mass in VGM. The result shows once again that a replacement of G by G* = G(1 - G M /2r) in general relativity will yield the corresponding result in VGM for the metric in vacuum.展开更多
Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the sol...Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy-momentum we obtain the value of energy.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.30370106)
文摘Eighty-four pollen samples were obtained for 80 taxa, of which, 13 species and one variety are from sect. Brachycalyx Sweet, 58 species and two varieties from sect. Tsutsusi Sweet, and six species from subgen. Pentanthera （G. Don） Pojarkova, respectively. Pollen morphology of all samples was observed using LM and SEM. Pollen grains are revealed to be spheroidal and tetrahedral with tricolporate apertures. Pollen sizes of subgen. Tsutsusi （Sweet） Pojarkova range from 37.67 μm to 61.06μm, and the exine sculptures are more or less compactly granulated. Pollen sizes are significantly different between sect. Brachycalyx and sect. Tsutsusi of subgen. Tsutsusi. Rhododendron tashiroi Maxim. of sect. Tsusiopsis Sleumer shows a close affinity to sect. Brachycalyx. Pollen size and exine are consistent with general morphology in differentiating species in sect. Tsutsusi. Rhododendron huadingense B. Y. Ding ＆ Y. Y. Fang, once placed as a member of sect. Brachycalyx, should be considered as a species in subgen. Pentanthera.
文摘A REDUCE code for the Newman-Janis algorithm is described. This algorithm is intended to include rotation into nonrotating solutions of the Einstein field equations with spherically symmetry or perturbed spherically symmetry and has been successfully applied to many spacetimes. The applicability of the code is restricted to metrics containing potentials of the form 1/r.
基金Supported by the National Natural Science Foundation of China(51574213,51074150)the Key Project of Chinese National Programs for Fundamental Research and Development(2012CBA01203)
文摘A new approach was proposed for grouping separation of 14 lanthanide rare-earth ions from their coexisting mixed aqueous solutions, by performing liquid-column elution using the aqueous solution containing 14 lanthanide rare-earth ions as the stationary phase and the dispersed organic oil droplets containing P507 extractant as the mobile phase. It was revealed that 14 lanthanide rare-earth ions could be separated into four groups, according to the lanthanide tetrad effect, respectively eluting out from the liquid column at different time in a certain order. Various effects including the saponification degree of P507, the concentration of P507 in organic phase, the length and inner diameter of the extraction column on the performance of grouping separation of rare-earth ions were discussed. The changes of the mass transfer coefficients were also investigated. The separation efficiency of the four groups of rareearth elements(REEs) was evaluated based on the elution resolution, Rs, of the elution peaks of La(Ⅲ),Gd(Ⅲ), Ho(Ⅲ) and Lu(Ⅲ), the four representative elements respectively from each of the four groups of REEs. Experimental results demonstrated that the separation of REEs by liquid-column elution mainly depended on the competitive adsorption of different rare-earth groups onto the surface of ascending P507 oil droplets. The affinity of different rare-earth groups with P507 extractant and a limited adsorption capacity of P507 molecules at the surface of the oil droplets ascending in liquid column play the important role. The present work highlights a promising technique for grouping separation of multiple lanthanide elements co-existing complex systems.
文摘Fractionations of rare earth elements (REEs) and the forming mechanisms in plants were studied using Triticum aestivum as plant material with application of exogenous REEs and hydroponic culture. REEs were significantly fractionated in different parts of Triticum aestivum. M-type tetrad effect could be observed in both root and shoot of Triticum aestivum, which might result from the different abilities of REEs to form phosphate precipitation. Middle REEs (MREEs), light REEs (LREEs) and heavy REEs (HREEs) were enriched in root, stem and leaf of Triticum aestivum, respectively. REE speciation calculations using VMINTEQ program show REEs in simulated xylem solution mainly exist as REE-EDTA^(- )and RE^(3+), but only HREEs are enriched in REE-EDTA^(-), while LREEs are enriched in the other REE species. It is suggested that the fractionation between LREEs and HREEs might be caused by the uptake of REE-EDTA^(-) in Triticum aestivum leaves, but might result from the uptake of the other REE species in their stems.
基金supported financially by the Research Bureau of Urmia University
文摘Intrusion of quartz-monzodioritic igneous bodies of Oligocene age into Eocene lithic crystal tufts and trachy-basalts resulted in the occurrence of a widespread argillic alteration zone in the Jizvan district （northern Iran）. Mineralogically, the argillie alteration zone includes minerals such as kaolinite, quartz, smectite, pyrophyllite, muscovite-illite, alunite, rutile, calcite, feldspar, chlorite, hematite and goethite. Therefore, the non-CHARAC behaviour for trace elements in the argillic samples is reflected in the non-chondritic Y/Ho and Zr/Hf ratios and the irregular REE patterns, which appear related to the tetrad effect phenomenon. The chondrite-normalized REE distribution patterns indicate both concave （W-shaped） and convex （M-shaped） tetrad effects in the argillic samples. Based on the field evidence and the results from geochemical studies, it can be concluded that the samples from the argillic alteration zone having high fourth tetrad effect values （〉0.30） were developed in the fault and breccia zones. The results indicate that factors such as preferential scavenging by Mn-oxides, crystallization of clay minerals, fluid-rock interaction, overprint of hypogene mineral assemblage by supergene ones, and the structural control, have all played an important role in the occurrence of tetrad effects in samples of the argillic zone in the Jizvan district.
基金financially supported by the National Natural Science Foundation of China (41372207)China Geological Survey (12120115069401, DD20160201-04, DD20160022-02, and DD20160101)the China Scholarship Councilprogram (201408110143)
文摘Walegen Au deposit is closely correlated with granitic intrusions of Triassic age, which are composed of granite and quartz porphyries. Both granite porphyry and quartz porphyry consist of quartz, feldspar and muscovite as primary minerals. WeaMy peraluminous granite porphyry （A/ CNK=1.10-1.15） is enriched in LREE, depleted in HREE with Nb-Ta-Ti anomalies, and displays subduction-related geochemistry. Quartz porphyry is strongly peraluminous （A/CNK=1.64-2.81） with highly evolved components, characterized by lower TiO2, REE contents, Mg#, K/Rb, Nb/Ta, Zr/Hf ratios and higher Rb/Sr ratios than the granite porphyry. REE patterns of quartz porphyry exhibit lanthanide tetrad effect, resulting from mineral fractionation or participation of fluids with enriched F and CI. LA- ICP-MS zircon U-Pb dating indicates quartz porphyry formed at 233±3 Ma. The ages of relict zircons from Triassic magmatic rocks match well with the detrital zircons from regional area. In addition, εHf（t） values of Triassic magmatic zircons from the granite and quartz porphyries are -14.2 to -9.1 （with an exception of ＋4.1） and -10.8 to -8.6 respectively, indicating a crustal-dominant source. Regionally, numerous Middle Triassic granitoids were previously reported to be formed under the consumption of Paleotethyan Ocean. These facts indicate that the granitic porphyries from Walegen Au deposit may have been formed in the processes of the closing of Paleotethyan Ocean, which could correlate with the arc-related magmatism in the Kunlun orogen to the west and the Qinling orogen to the east.
文摘The Guidong granitic complex is constituted by Luxi pluton, Xiazhuang pluton, Maofeng pluton, Sundong pluton, Aizi pluton and Siqian pluton, which intruded in Indosinian and early Yanshanian Periods. These plutons varies from each other not only in major element content, aluminium saturation index, but also in ∑REE, δEu, and LREE/HREE, （La/Yb）N, （La/Sm） N and （Gd/Yb） N ratios. Uranium mineralization is mainly hosted by strong peraluminous granites, which has undergone intense fluid-rock interaction, and their REE compositions are characterised by M-type tetrad effects and lower ∑REE, δEu value, LREE/HREE, （La/Yb） N, （La/Sm） N and （Gd/Yb） N ratios.
基金supported financially by the Research Bureau of Urmia University
文摘The Hizeh-Jan kaolin deposit(northwest of Varzeghan, East-Azarbaidjan Province, NW Iran) is a product of the alteration of Eocene andesitic rocks. Based on mineralogical examinations, kaolinite, quartz, smectite, pyrophyllite, muscovite-illite, alunite, calcite, diaspore, goethite and hematite are the most abundant mineral phases in this deposit. The geochemical indicators, such as Y/Ho and Zr/Hf, indicate the non-CHARAC(non-Charge-radius control) behavior of these pairs, which are likely to be due to the occurrence of the tetrad effect phenomenon in this deposit. Simultaneous concave and convex shapes in the chondrite-normalized REE distribution patterns are a remarkable feature of the kaolin samples. Bivariate diagrams of the size of the third tetrad effect(T_3) versus geochemical parameters such as Y/Ho, Nb/Ta and Zr/Hf ratios display two distinct populations for the kaolin samples. The first population is characterized by high T_3 values(>0.13), which are near or on the fault zone. The second population is characterized by low T_3 values(<0.13), and are farther from the fault zone. The obtained results from the geochemical data have furnished compelling evidence that fluidrock interaction, overprint of hypogene processes by supergene ones, and structural control, are key controlling factors for the occurrence of tetrad effects in REE distribution patterns in the Hizeh-Jan kaolin deposit.
基金supported financially by the Research Bureau of Urmia University
文摘Study of the concentration of major,trace,and rare earth elements(REE)in the Shahindezh karst bauxite deposit,northwestern Iran clarifies the relationship of the tetrad effect with geochemical parameters in the bauxite ores.The existence of irregular curves in the chondrite-normalized REE patterns as well as non-CHARAC behavior of geochemically isovalent pairs(Y/Ho)are related to the tetrad effect.The meaningful positive correlation between the sizes of the calculated T3 tetrad effect and some geochemical factors such as Y/Ho,ΣREE,La/Y,(La/Yb)N,and(LREE/HREE)N as well as some major oxides-based parameters like Al2O3+LOI/SiO2+Fe2O3,Al2O3/Fe2O3,Al2O3+LOI,IOL,and SiO2+Fe2O3indicate that the studied bauxite horizon was likely deposited by different(acidic and/or alkalic)solutions at different stages.The lower part of the studied horizon with a thickness of^4.7 m displays alkali characteristics whereas the upper parts of the horizon with a thickness of^5.3 m are characterized by more acidic conditions.These results are fully supported by the co-occurrence of convex-concave tetrad effect curves in the chondrite-normalized REE patterns.Therefore,the tetrad effect phenomenon used in this study has proved to be a good and reliable geochemical proxy to assess the conditions of the depositional environment in the Shahindezh bauxite ores.
文摘Paleozoic rocks in the Wadi El Sahu area are affected by many major faults in different directions.A reverse fault trending NE-SW is exposed for about 300 m of its length as it cuts through the Abu Hamata and Adedia formations on the south side of Wadi El Sahu.A secondary ascending hydrothermal solution carrying heavy metals and radioactive minerals passed through the fault plain and the surrounding fractures,forming mineralized and radioactive zone.The mineralized zone thickness ranges from 60 cm to 200 cm along the fault plain.These rocks were analyzed radiometrically using a portable gamma-ray spectrometer,chemically by employing ICP-ES and ICP-MS,as well as mineralogically by both binocular and Environmental Scanning Electron microscope.Gold content was also determined by fire assay.REE and U contents reached up to 2682 and 1216 ppm,respectively.Mineralogical investigations indicated the presence of uraninite,torbernite,autunite,sklodowskite,kasolite as uranium minerals,thorite as a thorium mineral,monazite,allanite and xenotime as REE-bearing minerals,zircon and columbite as accessory minerals,gold and nickel as precious and base metals,in addition to cassiterite,chalcopyrite,chalcocite and chrysocolla.High REE and U contents are attributed to the circulation of epigenetic U and REE-bearing hydrothermal solutions along the fault plain and its surrounding fractures.Hydrothermal alteration processes could then be confirmed by the presence of the M-type tetrad effect in the REE-patterns of the ferruginous sandstone.The non-chondritic ratio of Nb/Ta,Zr/Hf and Y/Ho in the studied sandstone may be attributed to the tetrad effect.The Ce and Eu anomaly with unusual REE-patterns was represented by the presence of conjugated M-W tetrad effects,indicating either the dual effect of hydrothermal solutions or groundwater with seawater.The results clarify that the tetrad-effects could be used as evidence for the environment of deposition and as an indication for gold mineralization.
基金the Deanship of Scientific Research at King Saud University for funding this work through research group number RG-1439-037。
文摘The Abu Dabbab albite granite(ADAG),in the central Eastern Desert of Egypt,hosts the most significant rare metal ore deposit in the northern part of the Neoproterozoic Arabian-Nubian Shield.Here,we report detailed field,petrographic,mineralogical and geochemical investigation of the ADAG,an isolated stock-like granitic body with sharp intrusive contacts against metamorphic country rocks,probably emplaced at about 600 Ma.The fine-grained porphyritic upper unit is a preserved remnant of the shallowly-emplaced apex of the magma chamber,whereas the medium-grained lower unit crystallized at deeper levels under subvolcanic conditions.The peraluminous leucocratic ADAG shares common geochemical characteristics with post-collisional intraplate A-type magmas.In addition to the conspicuous enrichment in Na2O,the ADAG is remarkable for its anomalous concentrations of Ta,Nb,Li,Hf,Ga,Sn,Zn and heavy rare-earth elements.Nb-Ta minerals in the ADAG are mixed with Fe-Mn oxides,forming black patches that increase in abundance toward of the base of the intrusion.Columbite-tantalite,cassiterite and wolframite are the most important ore minerals.Pronounced negative Eu anomalies(Eu/Eu*=0.10–0.24)reflect extreme magmatic fractionation and perhaps the effects of late fluid-rock interaction.The ADAG was most likely generated by partial melting of the juvenile middle crust of the ANS as the geotherm was elevated by erosional uplift following lithospheric delamination and it was emplaced at the intersection of lineations of structural weakness.Although formation of the ADAG and its primary enrichment in rare metals are essentially due to magmatic processes,late-stage metasomatism caused limited redistribution of rare metals.Fluid-driven subsolidus modification was limited to the apex of the magma chamber and drove development of greisen,amazonite,and quartz veins along fracture systems.
基金Project supported by the National Key Research and Development Project of China(2019YFC0605003)the StrategicPriority Research Program of Chinese Academy of Sciences(XDA02030100)。
文摘The deep understanding of 4f-correlated electron motion behavior is experimentally limited due to similar physicochemical properties of rare earth elements(REEs).While the solvent extraction behavior originating from the continuous occupation of 4f electrons along the lanthanide family provides a particular platform to probe the 4f electrons motion behavior and its correlations to their versatile functions.Herein,the complexation between REEs and the prototypical extractant of diethyl phosphoric acid(DEP)was substantially studied based on quantum mechanical calculation.The results firstly show that the average bond lengths between Ln and six coordinated oxygen atoms are consistent with lanthanide contraction phenomenon,and gadolinium break effect is also obviously observed.Secondly,the"tetrad effect"is figured out based on the subtle discrepancy of 4f electrons occupation,namely La-Nd,Sm-Eu,Gd-Dy and Ho-Lu.Specifically,the main composition is 4f5d6p for La-Nd,while the discrepancy is due to the increasing electrons in the 5d shell,while it is 4f5d for Pm-Eu.For Gd-Dy,their 4f orbitals accept little electrons and the donating electrons flow into 6s5d subshells due to the half-filled stability and the enhancement of shielding effect.The electrons donate into 5d6p subshells due to multiply electrons occupation of 4f orbitals for Ho-Lu.These detailed analyses obviously clarify the"tetrad effect"along the lanthanide family due to the different variation of 4f orbital occupation.It is expected that these microscopic understandings provide important guidance for the separation of REEs and the design of new extractants.
基金supported by the Macao Science and Technology Development Fund(No.FDCT 043/2014/A1)the financial FCT support(No.UIDB/50019/2020–IDL)。
文摘The widespread W-(Mo)-Sn-Nb-Ta polymetallic mineralization in Southeast(SE)China is genetically associated with Mesozoic highly fractionated granitic rocks.Such rocks have enigmatic mineralogical and geochemical features,making its petrogenesis an intensely debated topic.To better understand the underlying magma evolution processes,petrography,garnet chemistry and whole-rock major and trace element data are reported for Jurassic highly fractionated granitic rocks and associated microgranite and aplitepegmatite dikes from Macao and compared with coeval similar granitic rocks from nearby areas in SE China.Despite the fact that the most evolved rocks in Macao are garnet-bearing aplite-pegmatite dikes,the existence of coeval two-mica and garnet-bearing biotite and muscovite granites displaying more evolved compositions(e.g.,lower Zr/Hf ratios)indicates that the differentiation sequence reached higher degrees of fractionation at a regional scale.Although crystal fractionation played an important role,late-stage fluid/melt interactions,involving F-rich fluids,imparted specific geochemical characteristics to Macao and SE China highly fractionated granitic rocks such as the non-CHARAC(CHArge-and-RAdius-Controlled)behavior of trace elements,leading,for example,to non-chondritic Zr/Hf ratios,Rare Earth Elements(REE)tetrad effects and Nb-Ta enrichment and fractionation.Such process contributed to the late-stage crystallization of accessory phases only found in these highly evolved facies.Among the latter,two populations of garnet were identified in MGI(Macao GroupⅠ)highly fractionated granitic rocks:small grossular-poor euhedral grains and large grossular-rich skeletal garnet grains with quartz inclusions.The first group was mainly formed through precipitation from highly evolved Mn-rich slightly peraluminous melts under low-pressure and relatively low temperature(~700℃)conditions.Assimilation of upper crust metasedimentary materials may have contributed as a source of Mn and Al to the formation of garnet.The second group has a metasomatic origin related to the interaction of magmatic fluids with previously crystallized mineral phases and,possibly,with assimilated metasedimentary enclaves or surrounding metasedimentary strata.The highly fractionated granitic rocks in Macao represent the first stage in the development of granite-related W-(Mo)-Sn-Nb-Ta mineralization associated with coeval more evolved lithotypes in SE China.
文摘The muscovite granites at the study area are being emplaced into biotite granites and ophiolitic mélange settings. They occur in four exposures namely;Umm Seleimat, Sikait, Umm El Kheran and Umm Addebaa exposure. The presence of garnet and muscovite flakes may reflect the peraluminous nature of the studied muscovite granites. Petrographically, the studied granites are mostly subsolvus and consist of plagioclase, K-feldspars, quartz, muscovite and biotite. Garnet, zircon, allanite and opaques are accessories. The textural features of these granites are expressed by bent plagioclase lamellae, distorted microcline twinning, deformed mica flakes and development of myrmekite and recrystallization of feldspars into fine-grained aggregates. Umm Seleimat and Sikait exposures are more differentiated due to the presence of high content of K-feldspar and LREEs. The REE budget decreased from Umm Seleimat-Sikait exposures to Umm El Kheran-Umm Addebaa exposures as (514.5 - 495.6) to (195.9 - 197.7), respectively. Umm Seleimat-Sikait exposures have lower HREE/LREE (0.12 - 0.67), relative to Umm El Kheran-Umm Addebaa exposures (0.99 - 2.06). The studied granites revealed that the chondrite normalized REE patterns are the normal M-type of tetrad effect, where TE1,3 tetrad effect is higher than 1 in all samples which implies that there was an interaction between melt and water-haloid-rich fluid when these granites are crystallized from magma. Spectrometric values of Umm Seleimat and Umm Addebaa indicate that U content is more than Th content. Applying the U mobilization equation proved that the studied granites have been originated from a late magmatic phase of magma very rich in radioelements, also the majority of measurements lie above the zero line indicating that the studied granites affected with hydrothermal solutions rich in uranium than thorium which indicates uranium addition.
文摘The energy-momentum distributions of Einstein＇s simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann-Thomson, Landau-Lifshitz （LL）, Moller and Papapetrou energy-momentum complexes are used in general relativity. While Einstein and Bergmann-Thomson complexes give exactly the same results, LL and Papapetrou energy-momentum complexes do not provide the same energy densities. The Moller energy-momentum density is found to be zero everywhere in Einstein＇s universe. Also, several spacetimes are the limiting cases considered here.
基金Project supported by the National Natural Science Foundation of China (29875018)the Natural Science Foundation of Gansu Province (3ZS051-A25-050) the Doctorate Foundation of Northwestern Politechnical University (CX200309) and Gansu Key Laboratory of Polymer Materials
文摘PAMAM/lanthanide （Ⅲ） nanocomposite was studied by molecular simulation method. Molecular simulation enabled study of the lanthanide tetrad effect at atomic level. However, PAMAM dendrimer exhibiting unique properties such as nanometer size and highly functionalized terminal surface provided a novel space for lanthanide （Ⅲ） to show their peculiar tetrad effect. The results showed that total energies of PAMAM/lanthanide（Ⅲ） nanocomposites presented obvious tetrad effect and special double-double effect. Nd, Gd, and Er fell to the lower point and Gd fell to the lowest point in the TE-Ln curve with four groups. In order to explain the tetrad effect, kinetic energy （KE） and potential energy （PE） were analyzed. The KE curve consisted of three W-type parts （La - Pm, Pm - Tb, Tb - Tm, and the latter two W-type part were axial symmetry） and an exception part （Yb - Lu）. It also showed that the KE of odd atomic number was higher than the even one＇s with exception of Yb and Lu. Furthermore, decomposed potential energies gave out the atomic-level subtle difference of lanthanide which present more regulations for Eu（Ⅲ） - Lu（Ⅲ） compared with La（Ⅲ） - Sm（Ⅲ）. And also Ho-valley and three platforms （Sm - Eu, Td - Dy, Er - Tm） were discovered that refect the regular change of nanocomposite structures. Additionally, there are distinct correlations between Ebond and EInversion, EAngle and EVDW, Eworsion and ECoul, respectively. Therefore, PAMAM could be used in separation of lanthanide by changing conditions.
基金Project supported bythe National Key Science Foundation of China (40132010)the National Science Foundation of China(40642010 ,40772068)
文摘Guidong granitic complex is constituted by Luxi intrusion, Xiazhuang intrusion, Maofeng intrusion, Sundong intrusion, Aizi intrusion and Siqian intrusion, which emplaced in Indosinian and early Yanshanian Periods. These intrusions varied from each other not only in major element content, aluminium saturation index, but also in values of ∑REE, δEu, and LREE/HREE, (La/Yb)N, (La/Sm)N and (Gd/Yb)N. The Maofeng intrusion, which has the closest relationship with uranium mineralization, belongs to strong peraluminous granites. Having undergone much intense fluid-rock interaction, it is characterized by typical M-type tetrad effects and lowest values of ∑REE, δEu, LREE/HREE, (La/Yb)N, (La/Sm)N and (Gd/Yb)N ratios than other studied intrusions.
文摘In the framework of parallelism general relativity, the torsion axial-vector in the rotating gravitational field is studied in terms of the alternative Kerr tetrad. In thecase of the weak field and slow rotation approximation, we obtain that the torsion axial-vector possesses the dipole-like structure. Furthermore, the effect of massive neutrino spin precession in this field is mentioned.
文摘Based on the vector graviton metric theory of gravitation (VGM) suggested by one of the authors of this article, using the method of null tetrad and analytic continuation, this paper gives the metric of the rotating charged spherical mass in VGM. The result shows once again that a replacement of G by G* = G(1 - G M /2r) in general relativity will yield the corresponding result in VGM for the metric in vacuum.
文摘Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy-momentum we obtain the value of energy.
