Characteristics and genesis of maghemite in Chinese loess and paleosols:Mechanism for magnetic susceptibility enhancement in paleosols
Tianhu Chen a,b ,Huifang Xu b ,*,Qiaoqin Xie a ,Jun Chen c ,Junfeng Ji c ,Huayu Lu d
a
School of Natural Resources and Environment,Hefei University of Technology,Hefei,Anhui 230009,China
b
Department of Geology and Geophysics,University of Wisconsin,Madison,WI 53706,USA
c
Department of Earth Sciences,Nanjing University,Nanjing 210093,China
d
State Key Laboratory of Loess and Quaternary Geology,Institute of Earth Environment,Chinese Academy of Sciences,
Xi’an,Shaanxi 710075,China
Received 5March 2005;received in revised form 29June 2005;accepted 19September 2005
Available online 8November 2005
Editor:E.Boyle
Abstract
Morphological characteristics and microstructures of magnetic minerals extracted from Chinese loess and paleosols were investigated using powder X-ray diffraction (XRD)and high-resolution transmission electron microscopy (HRTEM).Our results indicate that maghemite in loess–paleosol sequences was transformed from magnetite through oxidation of magnetite.Maghemite transformed from eolian magnetite during chemical weathering has low-angle grain boundaries among maghemite nano-crystals.Some nano-crystalline maghemites with nanoporous texture resulted from microbe-induced precipitation of magnetite or transfor-mation of poorly crystalline ferric Fe (oxy)hydroxides in presence of Fe-reducing bacteria.Aggregates of euhedral maghemite nano-crystals were transformed from magnetite magnetosomes.Both microbe-induced nanoporous magnetite and microbe-produced magnetite magnetosomes are directly related to microbial activities and pedogenesis of the paleosols.It is proposed that the formation of nano-crystalline maghemite with superparamagnetic property in paleosol results in the enhancement of magnetic susceptibility,although the total amount (weight percent)of magnetic minerals in both paleosol and loess units is similar.Our results also show that nano-crystalline and nanoporous magnetite grains prefer to transform into maghemite in semi-arid soil environments instead of hematite,although hematite is a thermodynamically stable phase.This result also indicates that a decrease in crystal size will increase stability of maghemite.It is also inferred that surface energy of maghemite is lower than that of hematite.D 2005Elsevier B.V .All rights reserved.
Keywords:loess;paleosol;maghemite;biogenic magnetite;magnetic susceptibility;Transmission Electron Microscopy (TEM)
1.Introduction
Chinese loess is regarded as one of the best conti-nental record of paleoclimatic and paleoenvironmental
changes during the late Cenozoic era.There are numer-ous papers discussing paleoclimate changes based on magnetic susceptibility variations in the loess–paleosol sequences.The striking correlation between the varia-tions of color and magnetic susceptibility (MS)in Chinese loess–paleosol sequences and the marine oxy-gen isotope records have shown that the loess and paleosol units formed during glacial and interglacial
0012-821X/$-see front matter D 2005Elsevier B.V .All rights reserved.doi:10.1016/j.epsl.2005.09.026
*Corresponding author.Tel.:+16082655887;fax:+16082620693.
E-mail address:hfxu@https://www.doczj.com/doc/5912997853.html, (H.Xu).Earth and Planetary Science Letters 240(2005)790
–802
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episodes,respectively.The Chinese loess provides a complete record of East Asia paleoclimatic change over2.5Ma[1].The magnetic susceptibility of Qua-ternary loess can be easily measured and extensively used as proxy for paleoclimate[2–6].There are several proposed mechanisms for magnetic susceptibility en-hancement of the paleosol units,which include chem-ical weathering[7],magnetite deposition/accumulation [8],natural fire[9],pedogenesis[10,11],magnetotactic bacteria mineralization[12],and inorganic precipitation via iron reduction by iron-reducing bacteria[4].The changes of color and magnetic susceptibility in loess–paleosol sequences result from changing concentration and composition of iron oxides.Iron oxides and oxy-hydroxides including magnetite,goethite,hematite were first identified in loess–paleosol sequences by Heller and Liu[13]using optical microscopy.The existence of maghemite has also been supported by magnetic property and Mossbauer spectroscopy studies. Maghemite is also considered as a major carrier of magnetic susceptibility in loess–paleosol sequences [14–20].Because iron oxides are usually very fine grains with low crystallinity and low concentration in loess,traditional mineralogy analysis methods are not sensitive enough to identify them.Maher[4]and Van-denberghe et al.[21]used magnetic extraction methods to isolate strong magnetic iron oxides from soils.How-ever,it is difficult to identify the mineral composition of magnetically extracted fractions because both mag-netite and maghemite are very similar in their structures and chemical compositions[22–24].The magnetic minerals in loess–paleosol sequences were identified by indirect methods,such as magnetic property,Mo¨ss-bauer spectroscopy measurements,or differential ex-traction.It was considered that there are large amounts of ultra-fine magnetic particles in paleosol units[10,25].However,the mineral composition of the ultra-fine magnetic particles(i.e.,magnetite and/or maghemite)and their formation process were not well understood.Although it was considered that ultra-fine maghemite in the loess and paleosols is of authigenic origin and formed during pedogenesis,there are no direct observations of the maghemite.It is very difficult to understand formation of the maghemite and the mechanism for magnetic susceptibility enhancement in paleosol units without knowing details of this nano-meter-scale maghemite.
By analyzing magnetic minerals using transmission electron microscopy(TEM),Maher et al.have sug-gested that entirely euhedral and ultra-fine magnetic particles were attributed to magnetotactic bacteria bio-mineralization,and all the sub-micrometer particles with nanoporous structure were formed through inor-ganic precipitation by iron-reducing bacteria[4].TEM that can study mineral structures,microstructures,and compositions at the atomic scale is a very useful tool for studying textures and mineral reactions of the fine-grained Fe-oxide minerals[27–30].In this paper,we use this method to identify maghemite and magnetite minerals extracted from the loess–paleosol units,al-though differential chemical extraction of Fe method (citrate–bicarbonate–dithionite treatment)was also used to distinguish magnetite and maghemite[15,18].It was expected that the study at the nanometer scale will help us to understand mineral characteristics,mineral forma-tion mechanisms,and magnetic susceptibility enhance-ment in paloesol units,which will support studies in the areas of magnetic stratigraphy,geochemical processes of pedogenesis,and paleoclimate reconstruction in the loess–paleosol sequences.The study will also help us to understand role of ferric Fe reduction bacteria in the formation of magnetite.
2.Sample settings and experimental methods
Our samples were collected from following sites:the classic Luochuan,Huanxian and Xifeng sections.The extracted samples from one loess unit(L1),two paleo-sol units(S1,S3)and a red clay unit were used for this study.
Magnetic extraction methods were described previ-ously[31,32]:(1)adding10.0g of loess sample and a magnetic stir bar covered by Teflon into a1000-mL beaker;(2)stirring the loess/water suspension with a magnetic stirrer for2h at a rate of100rpm;(3)using non-magnetic tweezers to pick up the magnetic bar after stopping;the magnetic bar is covered a layer of dark and dark-brown powers;gently wash the bar three times with distilled water to remove clay minerals on surface;
(4)repeating the above processes until the magnetic bar does not take up any magnetic minerals from the bea-ker;the extracted minerals were used for scanning electron microscope(SEM),TEM and XRD analyses.
TEM investigation was carried out in the Depart-ment of Earth and Planetary Science,the University of New Mexico,USA.A JEOL2010HRTEM with an attached Oxford Instruments X-ray EDS system was used for TEM imaging and selected-area electron dif-fraction study[33].A JEOL2010F FASTEM with attached Oxford Instruments X-ray EDS system and Gatan Imaging Filtering(GIF)system was used for collecting electron energy-loss spectra that can identify oxidation states of transitional metals[34,35].The XRD analyses were carried out in the Structural Anal-
T.Chen et al./Earth and Planetary Science Letters240(2005)790–802791
ysis Center,Hefei University of Technology with a D/ max-RB type power diffractometer(Cu-target,40kV, 100mA,scan rate28/min).The SEM analyses were carried out in the Structural Analysis Center of the University of Science and Technology of China with
a HITACHI X-650SEM.
3.Identification and characteristics of maghemite 3.1.XRD identification of maghemite
Although the color of maghemite is the difference from that of magnetite,the crystal structure of maghe-mite(g-Fe2O3)is similar to that of magnetite(Fe3O4). The main structural and chemical difference between maghemite and magnetite is the existence of vacancies in maghemite,which lowers the symmetry of maghe-mite(primitive Bravais lattice)with respect to magne-tite(face-centered Bravais lattice).Further ordering of the vacancies results in a tetragonal supperlattice struc-ture with c=3a[53–57].In general,solid-state oxida-tion of magnetite may result in maghemite formation. Because magnetite and maghemite are very similar in their structures and their XRD patterns,diffraction peaks from magnetite nearly overlap with those from maghemite.Unit cell parameters for magnetite-and maghemite-based cubic setting are0.840nm and 0.835nm,respectively.A slight difference in unit cell parameters results in a slight shift of all peaks from maghemite towards higher angles with respect to the peaks from magnetite(Fig.1).When magnetite and maghemite coexist together,diffraction peak intensity and peak shape will change as their proportions change. In general,it is difficult to identify them by using powder XRD analysis alone.
There are various minerals in loess–paleosol se-quences,especially,quartz,calcite,and clay minerals. Concentration of magnetite and maghemite in loess–paleosol sequences is too low to be directly detected by XRD analysis based on counts of faint diffraction peaks from bulk samples.Wet magnetic extraction is an effi-cient method to enrich ferromagnetic minerals from the loess–paleosol samples for quantitative study of the magnetic minerals.The XRD patterns of magnetically extracted samples are displayed in Fig.2.The diffrac-tion peaks corresponding to magnetite and hematite are obvious.A majority of the extracted fractions are iron oxides with small amounts of quartz also present. Therefore,relatively pure iron oxide mixtures with low concentration of impurities can be obtained through the magnetic extraction.Fig.3that displays enlarged areas from Fig.2clearly shows that the diffraction peaks of magnetite/maghemite,such as220,511,and 440,obviously shift towards higher angles with respect to those from pure magnetite.These peaks are strong diffraction peaks from magnetite and maghemite.Con-tribution from hematite at these positions is very weak. Meanwhile,the104peak(d=2.69A?)of hematite in all samples does not shift,which indicates that peak shifts are caused by the presence of both magnetite and maghemite in the studied samples.The peak shifts are not from instrumental error.Therefore,the shifts of
220, Fig.1.Powder XRD patterns of synthetic magnetite and maghemite.Mt:maghemite(top);Mh:maghemite(middle);Mt+Mh:1:1mixtures of magnetite and maghemite(bottom).
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511,440peaks of the magnetic samples indicate that there are some amounts of maghemite in the extracted https://www.doczj.com/doc/5912997853.html,pared with the samples from the loess unit,diffraction peaks corresponding to magnetite from the paleosol are weaker,broader,and less sym-metrical.Our further TEM study in the next section will discuss evidence that these features result from the formation of nanometer-scale maghemite and
ox-
Fig.3.Powder XRD patterns of magnetically extracted minerals from the loess–palaeosol sequences.H–hematite;Mt–magnetite;Mh–maghemite;XFL1–Xifeng loess,unit L1;XF13–Xifeng palaeosol,unit S1;WS3–Wucheng paleosol,unit S3;RC–red clay layer;LCL1–Luochuan loess unit,L1;HXS1–Huanxian paleosol,unit
S1.
Fig.2.Powder XRD patterns of magnetically extracted fractions from the loess–paleosol sequences.H–hematite;Mt–magnetite;Mh–maghemite;Q–quartz;XFL1–Xifeng loess,unit L1;XF13–Xifeng paleosol,unit S1;WS3–Wucheng paleosol,unit S3;RC–red clay layer;LCL1–Luochuan loess,unit L1;HXS1–Huanxian paleosol,unit S1.
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idative transformation from magnetite to maghemite nano-crystals.
3.2.TEM identification and characteristics of maghemite
The magnetically extracted samples were directly deposited onto holey carbon-coated Cu grids that were used for TEM observations.The main structural difference between magnetite and maghemite is their Bravais lattice.Magnetite has a face-centered lattice(F) structure,whereas maghemite has a primitice(P)super-lattice structure.Therefore,{110}reflections that are extinct in magnetite will appear in maghemite[36].If we have[001]zone-axis high-resolution TEM (HRTEM)images from both magnetite and maghemite, the image from maghemite will display5.9-A?(110) lattice fringes,whereas the image from magnetite will only display3-A?(220)lattice fringes.Associated tech-niques of X-ray energy-dispersive spectra collected from a particular area can also help us to differentiate the oxides from silicate minerals.Selected area electron diffraction patterns can help us to differentiate the magnetite and maghemite from other iron oxide miner-als.In addition,electron energy-loss spectroscopy will help us to obtain the valence state of Fe.The integrated TEM study is a useful method for investigating the fine-grained magnetite and maghemite.We investigated 15magnetically extracted samples from loess–paleosol sequences using TEM and associated techniques.The maghemite has the following characteristics according to our TEM observations.
(1)Sub-micrometer-scale and smaller magnetic
grains that have morphological characteristics of
eolian origin were transformed into maghemite
that displays5.9-A?(110)lattice fringes(Fig.4).
Because the magnetite was completely oxidized
into maghemite,the resulting maghemite has
small crystalline domains with low-angle bound-
aries among the maghemite nano-crystals.The
arc-like streaking diffraction in its SAED pattern
clearly indicates the low-angle grain boundaries
in the transformed maghemite(Fig.4).The
angles measured from the SAED pattern are
less than108.
(2)Sub-micrometer grains from the loess unit that
have morphological characteristics of eolian ori-
gin,with edges and surfaces transformed into
maghemite that displays 5.9-A?(110)lattice
fringes.The grains still preserve single-crystal
morphology.However,SAED pattern with arc-
like streaking diffraction from the grain shows
multi-crystal domains with low-angle
grain Fig.4.High-resolution TEM image from an edge of the maghemite grain(inserted,upper-left corner).An SAED pattern from the grain and a [à110]zone-axis Fast Fourier Transform(FFT).The sample is from paleosol S1unit.
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boundaries (Fig.5).This kind of texture result from oxidative transformation of magnetite to maghemite.The single-crystal domain size of the maghemite is much smaller than that of the eolian magnetite grain.
(3)Some sub-micrometer grains display nanoporous texture that is composed of nano-crystalline maghemite (Fig.6).The SAED pattern from one of the grains shows powder diffraction rings.The powder diffraction pattern does not show a 110diffraction ring because of very weak 110refraction and highly disordered maghemite structure.Electron energy-loss spec-trum from the nanoporous grain shows an L
3
Fig.5.HRTEM image shows 5.9-A
?(110)lattice fringes of maghemite in a local area of an eolian grain.Inserted are low-magnification TEM image (upper-right corner)and SAED pattern (lower-left corner)of a partially oxidized magnetite.This sample is from loess L1
unit.
Fig.6.Bright-field TEM images of the maghemite from a paleosol unit.The right image is an enlarged area of the nanoporous maghemite.Inserted SAED pattern at upper-right corners is from the grain with a nanoporous structure.The first three diffraction rings are 200,111,and 220reflections.This sample is from Luochuan paleosol S1unit.
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edge peak at ~710eV,which indicates the pres-ence of ferric Fe in the structure [35,37].Such nanoporous structure is composed of randomly oriented maghemite nano-crystals.This sample is from the paleosol S1.4.Maghemite genesis
Maher et al.[4]suggested that all ferromagnets possessing nanoporous structure were formed from in-organic precipitation via iron reduction by iron-reduc-ing bacteria.Based on our systematic study on magnetically extracted samples using TEM,the ferro-magnetic minerals with nanoporous structure are more common in paleosol units than in loess units.It is proposed that such kind of magnetite was induced by microbes in soil environment.Microbes could generate a locally reducing environment that can promote mag-netite formation [56,57],which results in the formation of a composite of nano-crystalline magnetite and or-ganic matters produced by microbes.
We consider the nanoporous magnetite that has transformed into maghemite as biogenic magnetite.It is proposed that the nanoporous magnetite grains like that in Fig.6were resulted from dissimilatory reduction of ferric Fe and in situ precipitation of magnetite nano-crystals in locally reducing environments.Dissimilatory reduction of ferric Fe is a common reaction in soil environments [56,57].The other alternative for the nanoporous magnetite formation is the interaction be-tween ferric Fe-reducing bacteria and poorly crystalline ferric Fe (oxy)hydroxide (such as ferryhydrite)through dissolution/re-crystallization process and/or enzyme-mediated reactions between ferryhydrite and microbial reduced ferrous Fe.Such kind of microbe-induced magnetite nano-crystals can precipitate in a system containing bacteria of Geobacter sulfurreducences [58].Poorly crystalline ferric Fe precipitates are very reactive in microbial respiration process [59].The ferric Fe-reducing bacteria may transform ferryhydrite into magnetite and preserve nanoporous texture.The nano-pore areas could be rich in bio-organics.Decomposition of the organics and oxidation of the magnetite at solid state results in the formation of nanoporous maghemite.A nanoporous magnetite from a modern loess on basalt lava in the area of Albuquerque V olcanoes,New Mex-ico,shows small amounts of P and S besides Fe and O (Fig.7).A detailed mechanism for the nanoporous magnetite formation in water-unsaturated loess and the role of ferric Fe-reducing bacteria needs to be investigated in the future.
It was also observed that some nanoporous ferro-magnetic grains are nano-crystalline maghemite,result-ing,at least partially,from magnetite oxidation at solid state.Especially in Fig.8,a sub-angular ferromagnetic particle connected with a rutile crystal is obviously an eolian magnetite.At present,this grain is a multi-crystal maghemite with nanoporous structure.The SAED pat-tern from the transformed porous maghemite does not show random orientation of the maghemite nano-crys-tals.Therefore,not all the nanoporous structures resulted from biologically induced precipitation.The nanoporous maghemite can be formed through the oxidation of magnetite.A majority of magnetic iron oxides in large eolian grains are magnetite.It is difficult for maghemite to precipitate from water solution direct-ly.In general,maghemite is transformed from magne-tite through solid-state phase transformation,such as magnetite oxidation,lepidocrocite dehydration at high temperature,or organic-catalyzed goethite
dehydration
Fig.7.Left:TEM image shows a nanoporous magnetite from a modern loess in Albuquerque,NM.Right:X-ray energy-dispersive spectrum from area in left image shows Fe and oxygen with small amount of P that may be from bio-organics in the nanopores.The nanometer-scale pores here are worm-hole-like nanopores.Bright areas correspond to low electron density areas of nanopores.
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under surface/soil condition [38,39].Therefore,abun-dant magnetite–maghemite complexes in loess–paleo-sol sequences indicate oxidative transformation from eolian magnetite and authigenic magnetite to maghe-mite during pedogenesis.
In general,the extracted magnetic grains from loess units (e.g.,L1unit)are larger than those from paleosol units (e.g.,S1unit).Based on observations from TEM,optical microscope and XRD analyses,it is suggested that sub-micrometer magnetite grains were oxidized mainly into maghemite (Figs.4and 6)or magnetite–maghemite complexes (Figs.5and 8).Although pow-der XRD patterns show small amounts of hematite in the extracted magnetic samples (Figs.2and 3),red-dish hematite coatings (or rims)only occur in coarse magnetite grains according to optical microscopic ob-servation.Very fine grains and nano-crystals of mag-netite were mainly transformed into maghemite,even though hematite is thermodynamically more stable than maghemite.It is proposed that decreasing the crystal size of maghemite or increasing its surface area may increase its stability.Magnetite nano-crystals could be transformed into maghemite completely.Ox-idation products of magnetite at room temperature could be either maghemite or hematite,depending on original grain sizes of magnetite crystals.Of course,the size of the magnetite also affects its transformation rate.Synthetic experiments on magnetite oxidation show that its oxidation products could be dominated by maghemite or hematite depending on magnetite crystal sizes and impurities in the magnetite [40–42].Small magnetite grains (less than ~1A m)will favor maghemite formation during solid-state oxidative transformation [40–42].
Some magnetic grains show euhedral maghemite nanocrystals with a narrow range of size distribution (Figs.9and 10).Such maghemite was originally mag-netite from magnetotactic bacteria.They are biogenic magnetite according to criteria for identifying magneto-somes [4,43],although they are not arranged in chain-like shapes.This kind of maghemite is more common in the paleosol units than in loess units.Magnetosomes were found in the Chinese loess–paleosol sequences by Jia [12].Such kind of maghemite was suggested as a source of superparamagnetic particles and as the main mechanism of magnetic susceptibility enhancement.Maher et al.also considered euhedral magnetite grains with size range of 20–50nm as magnetosomes,
but
Fig.8.HRTEM image of an eolian grain that has transformed into maghemite.Its low-magnification TEM image (upper-right corner)shows nanoporous texture and an attached rutile crystal.Its SAED pattern (lower-right corner)shows 110reflection from maghemite structure.This sample is from paleosol S1unit.
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Fig.9.TEM image inserted SAD (right upper corner)and lattice fringe (right down corner)shows narrow range of size distribution and euhedral maghemite crystals that were magnetite from magnetotactic bacteria or biogenic
magnetite.
Fig.10.HRTEM image shows a maghemite single crystal with (110)lattice fringes that was a magnetite grain from magnetotactic bacteria.
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argued that they only play a secondary role in the magnetic susceptibility enhancement because of their small volume percentage in the loess–paleosol se-quences[4,44,45].The results of the TEM investigation indicate that all the magnetite nano-crystals similar to magnetosomes display(110)superstructure lattice fringe in maghemites(Fig.10).Such kind of maghe-mite is directly related to microbial biomineralization. The maghemite nano-crystals were transformed from the oxidation of magnetosomes.Experimental study also confirms that nanometer-size magnetite can be easily oxidized into maghemites under room tempera-ture condition[46].
Based on the above results,it can be inferred that the oxidation product of magnetite nano-crystals is maghemite at low temperature.Therefore,superpara-magnetic particles in loess–paleosol sequences should be maghemite instead of magnetite.This result also confirms previous suggestions and magnetic property studies of the loess–paleosol sequences.It can be in-ferred that nanometer-scale maghemite is more stable than magnetite in the oxidizing environment.Maghe-mite nano-crystals may be more stable than hematite at room temperature in dry environments,although Dia-konov suggested that maghemite will be stable with respect to hematite when the nano-crystals of maghe-mite reach surface areas of about535m2/g[26]. McHale et al.[47]had found that g-Al2O3nano-crystal is more stable than a-Al2O3nano-crystal because of the lower surface energy of g-Al2O3with respect to that of a-Al2O3.The structure of g-Fe2O3is same as that of g-Al2O3,and so is the structure of a-Fe2O3.In a similar way,the surface energy of g-Fe2O3should be lower than that of a-Fe2O3[48].As a result,decreasing the crystal size of maghemite will increase its stability at room temperature.
Because maghemite was formed from low-tempera-ture oxidation of magnetite,maghemite concentration in loess–paleosol sequences relates to the concentration of magnetite formed during pedogensis and grain size of eolian magnetite.Both magnetite magnetosomes and precipitated magnetite with nanoporous texture induced by iron-reducing bacteria are related to microbial activ-ity in the soil environment.The size distribution of eolian origin magnetite grains is related to the intensity of the winter monsoon winds.Therefore,the concen-tration of authigenic magnetite,the weathering of the eolian magnetite,and the concentration of maghemite can be used as signatures of paleoclimate changes. Deng et al.[20]also suggested that strong pedogenesis will result in the high concentration and intense oxida-tion of magnetite.5.Mechanism for the magnetic susceptibility enhancement
Maher[49]pointed out that the susceptibility of magnetite with crystal size of~10nm will be about four times higher than that with crystal sizes of several micrometers.The critical size for maghemite to be superparamagnetic is about30–50nm[46].Our TEM results show that there are nanoporous maghemite grains composed of maghemite nano-crystals in paleo-sol samples(Fig.6).Such kind of maghemite is directly related to microbial activity during pedogenesis.Our TEM results also provide the microstructural evidence for chemical weathering from magnetite to maghemite. Submicrometer-size eolian magnetite can be trans-formed into nanometer maghemite in the pedogenic process(Fig.8),which changes ferromagnetic grains into superparamagnetic nano-crystals.We propose that maghemite has similar size-dependent magnetic suscep-tibility,although there is no reported data showing the relationship between magnetic susceptibility and its crystal sizes.It can be inferred that although the total amount of ferromagnetic particles(weight percentage) in paleosol units does not show an obvious increase with respect to that in loess units,magnetic suscepti-bility can be enhanced several times because of the formation of nano-crystalline maghemite.
It should be pointed out that although the overall particle size of the nanoporous maghemite is about micrometer or sub-micrometer scale,the crystalline domains are at the scale of ten or several tens of nanometers.The nano-crystal domains in weathered magnetite also enhance magnetic susceptibility.This process is related to chemical weathering.However, the role of microbes and bio-organics play an important role.This phenomenon may result in a disagreement between the crystal size of magnetic carriers in magne-tism analyses and selected grain sizes for magnetic susceptibility analyses.The magnetic property study of loess samples suggests that magnetic susceptibility enhancement in paleosols results from authigenic fine-grained magnetite crystals(that has transformed to maghemite).However,Han et al.[50]argued that the content of nanometer-scale grains in loess–paleosol sequences is very small and its contribution to magnetic susceptibility is less than5%according to susceptibility analyses from different grain size fractions of typical loess and paleosol units.Contributions to magnetic susceptibility are mainly from larger than1-A m fraction grains in loess sample,because the loess unit contains more coarse grains(Fig.11).Fig.11A shows that there is no obvious change in magnetic susceptibility for
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various fractions of the loess sample.However,the magnetic susceptibility for 1-A m and less than 1-A m fraction samples from paleosol sample increases signif-icantly with respect to the loess sample,which indicates magnetic susceptibility enhancement in these size frac-tions.Han et al.suggested that magnetic susceptibility enhancement should be related to iron oxide evolution during pedogenesis but could not provide a detailed explanation for these processes.Our TEM results show-ing nano-crystalline maghemite explain the enhance-ment of the magnetic susceptibility in fine-grained fractions because of the formation of maghemite nano-crystals.
Recently,many authors have proposed the effect of microstructure and crystal size on their magnetic sus-ceptibility anomalies.Harrison et al.[51]directly mapped the nanometer magnetic structure with elec-tron holograms in TEM and gave an excellent expla-nation for the magnetic anomaly in their nano-structured magnet.McEnroe et al.[52]also found that the mechanism explaining the magnetic anomaly in massive ilmenite rock was the formation of nano-meter-scale lamella of hematite and ilmenite during the exsolution of hematite–ilmenite solid solution.Brown and O’Reilly [42]found that magnetic susceptibility enhancement of pulverized natural titanomagnetite is related to nano-structure resulting from stress during ball-milling.Banfield et al.[23]proposed a connection between intergrown structure of massive magnetite–maghemite at the nano-meter scale and its strong
magnetic property.All the previous results indicate that nano-structures of magnetic grains may cause magnetic susceptibility enhancement for magnetite and maghemite.6.Conclusions
Based on our direct observations in TEM and XRD studies,it can be concluded that sub-micrometer-and nanometer-size magnetites were completely oxidized into maghemite during the pedogenic (soil formation)process.The oxidized products of sub-micrometer mag-netite have multi-domain structure that is composed of maghemite nano-crystals.Biogenetic magnetite can be preserved as maghemite in loess–paleosol sequences that formed during solid-state transformation from mag-netite to maghemite.Some nano-crystalline maghe-mites with nanoporous texture resulted from microbe-induced precipitation of magnetite or transformation of poorly crystalline ferric Fe (oxy)hydroxides by Fe-re-ducing bacteria.The crystal size of maghemite will affect its stability.Maghemite with small size (~nano-meter scale)is more stable than that with large size.Superparamagnetic particles composed of maghemite nano-crystals are the main carrier of magnetic suscep-tibility in the loess and paleosols.We suggest the formation of nano-structured maghemite and biogenic magnetite are responsible for the magnetic susceptibil-ity enhancement in the paleosol units.HRTEM with associated analytical techniques is a useful tool
for
Fig.11.Contribution of different size fractions to magnetic susceptibility and magnetic susceptibility of different size fraction samples from Xifeng section (calculated from the data in [50]).(A)Magnetic susceptibility of different size fractions;(B)contribution of different grain size fractions to magnetic susceptibility.
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studying mechanisms for the magnetic susceptibility enhancement in paleosols.
Acknowledgement
The work was supported by the National Natural Science Foundation of China(40331001,40472026), the Outstanding Overseas Chinese Scholars Fund of the Chinese Academy of Sciences(2003-1-7),and the Na-tional Science Foundation(EAR02-0210820).The authors thank the Department of Geology and Geo-physics of the University of Wisconsin for partial sup-port of this study.The authors also thank Joe Mason, Ed Boyle,and an anonymous reviewer for providing helpful comments and suggestions.
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第一讲：集合与区间的概念及其表示法 知识点一、区间的概念 设 a ，b 是实数，且 a ＜b ，满足 a ≤x ≤b 的实数 x 的全体，叫做闭区间， 记作 [a ，b ]，即，[,]{|}a b x a x b =≤≤。如图： a ， b 叫做区间的端点．在数轴上表示一个区间时，若区间包括端点，则端点用实心点表示；若区间不包括端点，则端点用空心点表示． 全体实数也可用区间表示为(－∞，＋∞)，符号“＋∞”读作“正无穷大”，“－∞”读作“负无穷大”，即(,)R =-∞+∞。 知识二、元素与集合：指定对象的全体叫“集合”，简称“集”，用大写英文字母A 、B 、C 等表示，其中的每个对象叫“元素”，用小写英文字母a 、b 、c 表示 1.集合元素的特性： 集合中元素的从属性要明确 反例：大树、好人 集合中元素必须能判定彼此 反例：2，2 集合中元素排列没有顺序 如：{1,2,3}{2,1,3}= 例1、判断下列各组对象能否组成集合： （1）不等式的解； （2）我班中身高较高的同学； （3）直线上所有的点； （4）不大于10且不小于1的奇数。 练习1.给出下列说法： （1）较小的自然数组成一个集合； （2）集合{1，-2，3，π}与集合{π，-2，3，1}是同一个集合； （3）若∈a R ，则a ?Q ； （4）已知集合{x ，y ，z }与集合{1，2，3}是同一个集合，则x =1，y =2，z =3 其中正确说法个数是（ ） 例2.集合A 是由元素n 2-n ，n -1和1组成的，其中n ∈Z ，求n 的取值范围。 例3.已知M=｛2,a,b ｝N=｛2a,2,｝且M=N ，求a,b 的值 练习2.已知集合M={a,a+d,a+2d},N={a,aq,aq 2},a≠0,且M 与N 中的元素完全相同，求d 和q 的值。 320x +>21y x =-2 b
区间的概念 【教学目标】 1. 理解区间的概念，掌握用区间表示不等式解集的方法，并能在数轴上表示出来． 2. 通过教学，渗透数形结合的思想和由一般到特殊的辩证唯物主义观点． 3. 培养学生合作交流的意识和乐于探究的良好思维品质，让学生从数学学习活动中获得成功的体验，树立自信心． 【教学重点】 用区间表示数集． 【教学难点】 对无穷区间的理解． 【教学方法】 本节课主要采用数形结合法与讲练结合法．通过不等式介绍闭区间的有关概念，并与学生一起在数轴上表示两种不同的区间，学生类比得出其它区间的记法．在此基础上引导学生用区间表示不等式的解集，为学习用区间法求不等式组的解集打下坚实的基础．【教学过程】
新课区间不包括端点，则端点用空心点表示． 全体实数也可用区间表示为(－∞，＋∞)，符 号“＋∞”读作“正无穷大”，“－∞”读作“负无 穷大”． 例1用区间记法表示下列不等式的解集： (1) 9≤x≤10；(2) x≤0.4． 解(1) [9，10]；(2) (－∞，0.4]． 练习1用区间记法表示下列不等式的解集， 并在数轴上表示这些区间： (1) －2≤x≤3；(2) －3＜x≤4； (3) －2≤x＜3；(4) －3＜x＜4； (5) x＞3；(6) x≤4． 例2用集合的性质描述法表示下列区间： (1) (－4，0)；(2) (－8，7]． 解(1) {x | －4＜x＜0}；(2) {x | －8＜x≤7}． 练习2用集合的性质描述法表示下列区间， 并在数轴上表示这些区间： (1) [－1，2)；(2) [3，1]． 例3在数轴上表示集合{x|x＜－2或x≥1}． 解如图所示． 用表格呈现相应的 区间，便于学生对比记 忆． 教师强调“∞”只是 一种符号，不是具体的 数，不能进行运算． 学生在教师的指导 下，得出结论，师生共 同总结规律． 学生抢答，巩固区 间知识． 学生代表板演，其 它学生练习，相互评价． 了铺垫． 学生理解无 穷区间有些难 度，教师要强调 “∞”只是一种 符号，并结合数 轴多加练习。 三个例题 之间，穿插类似 的练习题组，使 学生掌握不等 式记法，区间记 法，数轴表示三 者之间的相互 转化．逐层深 入，及时练习， 使学生熟悉区 间的应用． x 01 －1 －2
区间的概念教学设计
新课 新课 设a，b 是实数，且a＜b． 满足a≤x≤b 的实数x 的全体，叫做闭区 间，记作 [a，b]，如图． a，b 叫做区间的端点．在数轴上表示一个区 间时，若区间包括端点，则端点用实心点表示；若 区间不包括端点，则端点用空心点表示． 全体实数也可用区间表示为(－∞，＋∞)，符 号“＋∞”读作“正无穷大”，“－∞”读作“负无 穷大”． 例 1 用区间表示不等式 3x＞2+4x 的解集， 并在数轴上表示出来。 解：解不等式 3x＞2+4x 得： x＜ -2 所以用区间表示不等式的解集是 (-∞，-2) 在数轴上表示如图 练一练：用区间表示不等式 4x＞2x+4的解 集，并在数轴上表示出来。 教师讲解闭区间， 开区间的概念，记法和 图示，学生类比得出半 开半闭区间的概念，记 法和图示． 用表格呈现相应的 区间，便于学生对比记 忆． 教师强调“∞”只是 一种符号，不是具体的 数，不能进行运算． 学生在教师的指导 下，得出结论，师生共 同总结规律． 学生抢答，巩固区 间知识． 学生代表板演，其 教师只讲 两种区间，给学 生提供了类比、 想象的空间，为 后续学习做好 了铺垫． 学生理解无 穷区间有些难 度，教师要强调 “∞”只是一种 符号，并结合数 轴多加练习。 三个例题 之间，穿插类似 的练习题组，使 学生掌握不等 式记法，区间记 法，数轴表示三 者之间的相互 转化．逐层深 入，及时练习，
例2 已知集合A=( 0 ，3 )，集合B=[ -1， 2 ]，求 A∩B ，A∪B 。 解：两个集合的数轴表示如图所示： 察图形知： A∩B = ( 0 ，2 ] A∪B = [ -1 ，3 ) 练一练 1、已知集合A=[ -3 ，4 ]，集合B=[ 1， 6 ]，求 A∩B ，A∪B 。： 它学生练习，相互评价． 同桌之间讨论，完 成练习． 使学生熟悉区 间的应用． 小 结 填制表格： 集合区间区间名称数轴表示 {x|a＜x＜b} {x|a≤x≤b} {x|a≤x＜b} {x|a＜x≤b} 集合区间数轴表示 {x | x＞a } {x | x＜a } {x | x≥a } {x | x≤a} 师生共同完成表格．通过表格 归纳本节知识， 有利于学生将 本节知识条理 化，便于记忆。作业布置
课 题：2.1.2函数－区间的概念及求定义域的方法 教学目的： 1．能够正确理解和使用“区间”、“无穷大”等记号；掌握分式函数、根式函数定义域的求法，掌握求函数解析式的思想方法； 2．培养抽象概括能力和分析解决问题的能力； 教学重点：“区间”、“无穷大”的概念，定义域的求法 教学难点：正确求分式函数、根式函数定义域 授课类型：新授课 课时安排：1课时 教 具：多媒体、实物投影仪 教学过程： 一、复习引入： 函数的三要素是：定义域、值域和定义域到值域的对应法则；对应法则是函数的核心(它规定了x 和y 之间的某种关系)，定义域是函数的重要组成部分（对应法则相同而定义域不同的映射就是两个不同的函数）；定义域和对应法则一经确定，值域就随之确定 前面我们已经学习了函数的概念，，今天我们来学习区间的概念和记号 二、讲解新课： 1．区间的概念和记号 在研究函数时 ,常常用到区间的概念，它是数学中常用的述语和符号. 设a,b ∈R ,且a 课题：2.1.2函数－区间地概念及求定义域地方法教学目地： 1．能够正确理解和使用“区间”、“无穷大”等记号；掌握分式函数、根式函数定义域地求法,掌握求函数解析式地思想方法； 2．培养抽象概括能力和分析解决问题地能力； 教学重点：“区间”、“无穷大”地概念,定义域地求法 教学难点：正确求分式函数、根式函数定义域 授课类型：新授课 课时安排：1课时 教具：多媒体、实物投影仪 教学过程： 一、复习引入： 函数地三要素是：定义域、值域和定义域到值域地对应法则；对应法则是函数地核心(它规定了x和y之间地某种关系),定义域是函数地重要组成部分（对应法则相同而定义域不同地映射就是两个不同地函数）；定义域和对应法则一经确定,值域就随之确定 前面我们已经学习了函数地概念,,今天我们来学习区间地概念和记号 二、讲解新课： 1．区间地概念和记号 在研究函数时,常常用到区间地概念,它是数学中常用地述语和符号. 设a,b∈R ,且a 这样实数集R 也可用区间表示为(-,+),“”读作“无穷大”,“-”读作“负无穷大”,“+∞”读作“正无穷大”.还可把满足x ≥a,x>a,x ≤b,x= 课题：2.1.2函数－区间的概念及求定义域的方法 教学目的： 1．能够正确理解和使用“区间”、“无穷大”等记号；掌握分式函数、根式函数定义域的求法，掌握求函数解析式的思想方法； 2．培养抽象概括能力和分析解决问题的能力； 教学重点：“区间”、“无穷大”的概念，定义域的求法 教学难点：正确求分式函数、根式函数定义域 授课类型：新授课 课时安排：1课时 教具：多媒体、实物投影仪 教学过程： 一、复习引入： 函数的三要素是：定义域、值域和定义域到值域的对应法则；对应法则是函数的核心(它规定了x和y之间的某种关系)，定义域是函数的重要组成部分（对应法则相同而定义域不同的映射就是两个不同的函数）；定义域和对应法则一经确定，值域就随之确定 前面我们已经学习了函数的概念，，今天我们来学习区间的概念和记号二、讲解新课： 1．区间的概念和记号 在研究函数时,常常用到区间的概念，它是数学中常用的述语和符号. 设a,b∈R ,且a 这样实数集R 也可用区间表示为(-,+),“”读作“无穷大”，“-”读作“负无穷大”，“+∞”读作“正无穷大”.还可把满足x ≥a ，x>a ，x ≤b ，x=函数区间的概念及求定义域的方法
高中数学教案——函数-区间的概念及求定义域的方法
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