What Grain Alignment can Tell about Circumstellar Disks and Comets

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What Grain Alignment Can Tell About Circumstellar Discs and Comets https://www.doczj.com/doc/9711120380.html,zarian Canadian Institute for Theoretical Astrophysics and Depatment of Astrophysics of University of Toronto,Toronto,Canada,ON M5S 1A1e-mail:lazarian@cita.utoronto.ca ABSTRACT Grain alignment theory suggests that grains should be aligned in circumstellar regions and the observational data available supports this conclusion.We discuss the alignment of grains via (1)magnetic relaxation,(2)mechanical processes,and (3)radiative torques.We show that ferromagnetic relaxation is likely to be more important than superparamagnetic relaxation if the dust in circumstellar regions is similar to species recently captured in Earth atmosphere.Out?ows and stellar winds provide grain streaming along magnetic ?eld lines and therefore mechanical alignment competes with the ferromagnetic and radiative alignments.We estimate measures of grain alignment in circumstellar regions,comets and interplanetary space and conclude that in many circumstellar regions and in the interplanetary space radiative torques may constitue the major alignment mechanism which aligns grain longer axes perpendicular to the direction of magnetic ?eld.Observations in submillimeter and microwave ranges are suggested as a means of disentangling e?ects of multiple scattering from those related to aligned grains.

Subject headings:ISM:Magnetic ?eld,Polarimetry,Comets,Interplanetary Dust,Zodiacal Light

1.Introduction

Recent years have been marked by signi?cant advances in understanding of grain alignment processes (see Roberge 1996,Lazarian,Goodman &Myers 1997).A number of

new alignment mechanisms have been suggested(e.g.Draine&Weingartner1996,1997, Lazarian1995a)and traditional mechanisms underwent serious revision(see Lazarian

&Draine1997).This process was motivated by new interstellar polarization data(e.g. Goodman1995,1996)and,unfortunately,has not made the appropriate inpact upon the areas beyond the interstellar domain.

At the same time the number of puzzling results is growing in the areas of comet and circumstellar polarimetry,where it is customary to believe that polarization arises from light scattering on randomly oriented dust grains.In this paper we show that some of these puzzles vanish if grain alignment is accounted for.

Although models of circumstellar regions that invoke aligned grains have been occasionally discussed in the literature(see Dolginov&Mytrophanov1976,Pudritz,1986, 1988),their applicability was highly questionable in the absence of the reliable grain alignment theory(see Bastien1988).On the contrary,recent theoretical advances indicate that grain alignment is likely to be ubiquitous and therefore must be accounted for while modeling circumstellar polarization and the polarization from comets.

In what follows we identify mechanisms of alignment that are most e?cient in circumstellar regions and in comet atmospheres(section2),then touch upon the relation between grain alignment and linear and circular polarization(section3).In section4we discuss grain alignment in circumstellar regions,comets and in interplanetary space.Ways of separating the e?ects of multiple scattering and those of grain alignment are discussed in section5and we summarize our results in section6.Important but more specialized discussion of ferromagnetic versus superparamagnetic relaxation is given in the Appendix.

2.Grain Alignment

Discovered half a century ago(see Hiltner1949,Hall1949),grain alignment continues to be a tough problem for theorists.The dynamics of rapidly rotating dust particles is being in?uenced both by numerous processes that include gaseous and ion bombardment,plasma e?ects,interactions with starlight etc.(see more detail in Draine&Lazarian1998a,1998b). Chemical processes,e.g.H2formation that take place on grain surfaces also in?uence grain dynamics(Purcell1979,Lazarian1995b).Moreover,observations suggest a strong dependence of the alignment e?ciency on grain sizes.Indeed,interstellar observations can

be only explained if grains with sizes>10?5cm are aligned,while smaller grains are not2 (Kim&Martin1995).

In spite of all these di?culties substantial progress has been recently achieved in understanding of grain alignment processes.A list that includes six major mechanisms was presented in Lazarian,Goodman&Myers(1997)and a number of“exotic”mechanisms have been described there as well.Below we discuss only those of the mechanisms that can be relevant for grain alignment in circumstellar regions and in comet atmospheres.We claim that to succeed in these environments the process must be fast.Therefore slow processes that may well work in the interstellar medium are likely to fail in circumstellar regions.For instance,we do not discuss paramagnetic alignment of suprathermal grains(Lazarian& Draine1997)that slowly but steadily alignes grains over many gaseous damping times.

To characterise the alignment we use the Raylegh reduction factor(Greenberg1968)

R=3

3

,(1)

where ... denotes the ensemble average,βis the angle between grain axis of maximal inertia and the direction of alignment.We show below that often it is magnetic?eld that de?nes direction,even for non-magnetic alignment mechanisms.

In general,grain alignment is non-equilibrium process.Therefore in dark clouds where “classical”grains are in thermodynamic equilibrium with the ambient gas no alignment is observed(Lazarian,Goodman&Myers1997).To align grains,i.e.to decrease the enthropy of their distribution,the enthropy of some other system(systems)must increase.

2.1.Paramagnetic alignment

The oldest of the alignment mechanisms is the process of paramagnetic relaxation suggested by Davis&Greenstein(1951)and later modi?ed by Purcell(1979),who observed that grains may rotate much faster that was originally thought.To understand the essence of this mechanism it is su?cient to consider a sherical grain which angular velocity makes angleβwith magnetic?eld B.The component of angular velocity perpendicular to B, i.e.ωsinβ,will cause oscillating remagnetization of the grain,whileωcosβwill not cause oscillations of magnetization.As oscillating magnetization entails dissipation,the componentωsinβdecreases,whileωcosβstays the same.As the result,βdecreases.

Thus magnetic?eld causes anisotropy in the distribution of grain angular momenta.As non-spherical grains tend to rotate about their axes of maximal moment of inertia(Purcell 1979)the anisotropy in the distribution of angular momentum is being translated into the anisotropy of the distribution of grain longer axes.

Leaving aside the mathematical theory of alignment(Lazarian1997,1998,Roberge& Lazarian1999),that accounts for grains being non-spherical and internal relaxation being not complete,we may claim that the alignment happens on the time scale of paramagnetic relaxation,which for ordinary paramagnetic grains is rather long,e.g.

t al=4×1012K?1?13B?2?5a2?5s,(2) where the lower indexes used to denote the normailization values.For instance,the K function,which is the ratio of the imaginary part of grain magnetic susceptibilityχ(ω)to its angular velocityω,was normalized to10?13s.In other words,K?13≡K/(10?13s). Similarly,magnetic?eld is normalized by10?5G and grain size a?5≡a/(10?5cm).

Grain rotation can be randomized by gaseous bombardment on time scales

a?5s,(3)

t gas=6×1011n?110T?1/2

gas,5000

where n10≡n/(3cm?3),T gas,5000≡T gas/(5000K).In the equation above the environmental parameters are taken rather arbitrary and for particular cases the more relevant values should be substituted.Moreover the estimate for t gas must be reduced nearly an order of magntitude if gas is ionized(see Anderson&Watson1993,Draine&Lazarian1998a).The latter e?ect is the consequence of higher e?ciency of plasma interactions with a charged grain compared to gas-grain interactions.

To obtain e?cient paramagnetic alignment t al should be much less than t gas.Therefore grains with superparamagnetic and ferromagnetic inclusions(Jones&Spitzer1967,Mathis 1986,Martin1995,Draine1996,Draine&Lazarian1998c)are to be considered.

How abundant ferro-and superparamagnetic grains in comet environment and circumstellar regions is not clear.The presence of small F eNi and F eNiS inclusions in particles coming from the interplanetary space has been recently reported(Bradley1994) and this supports the case for“super”grains(Goodman&Whittet1996).Our analysis of the particle image in?gure1in Goodman&Whittet(1996)indicates that most of the inclusions are too large to exhibit superparamagnetic response forω>106s?13(see

Appendix).However,our calculations in the Appendix prove that the ferromagnetic response of grains with iron inclusions provides enhancement of the paramagnetic relaxation by a factor103?104if the volume?lling factor of inclusions is～0.01as we roughly estimated from the?gure in Goodman&Whittet(1996).The decrease of paramagnetic alignment time t al by the factor104arising from ferromagnetic inclusions makes t al～4×108s.This seems su?cient for circumstellar alignment but may be slow for comet grain alignment.

2.2.Mechanical Alignment

Another mechanism of grain alignment stems from mechanical interaction of grains with streaming gas.Suggested initially by Gold(1952)for grains rotating with thermal velocities,the mechanical alignment has been recently proved to be e?cient for grains rotating with much higher velocities(Lazarian1994a,Lazarian1995a,Lazarian&Efroimsky 1996,Lazarian,Efroimsky&Ozik1996).Such high(suprathermal)velocities arise from uncompensated quasi-regular torques,e.g.from torques arising from H2formation over catalytic sites on grain surface(Purcell1975,1979).These sites act as rocket engines and their action spins up the grain.The number of sites over grain opposing surfaces,in general, is di?erent and this causes a regular spin-up.

The original Gold’s idea is based on the observation that when a?ow of gas interacts with an elongated grain the angular momentum deposited with the grain tends to be directed perpendicular to the?ow.Accounting for suprathermal rotation and the presence of magnetic?eld makes the process of alignment a bit more involved(see Lazarian1995a).

The necessary condition for the mechanical alignment is the supersonic relative motion of grains and gas.If this condition is not satis?ed isotropic gaseous bombardment randomizes grains(see eq.(25)in Lazarian1997a).The rule of thumb for mechanical alignment is that the process tends to minimize gas-grain cross section of interaction4.

It is easy to see that,unlike paramagnetic alignment,the mechanical one is not directly connected with the action of the ambient magnetic?eld.However,in many cases mechanical processes align grains either parallel or perpendicular to the direction of magnetic?eld. This is the concequence of grain rapid precession about magnetic?eld.Indeed,a rotating grain aquires a magnetic moment via the Barnett e?ect(Dolginov&Mytrophanov1976, Purcell1979)and this magnetic moment precesses in the external magnetic?eld with the

period

t L=2×105B?1?5a2?5s.(4) If t L is much shorter than the time of mechanical alignment t mech,external magnetic?eld de?nes the axis of alignment.

t mech is di?erent for thermally and suprathermally(much faster than thermally) rotating grains.In the former case t mech can be de?ned as a time during which the angular momentum of a grain changes by the value of its thermal angular momentum

J th=(kT gas/I)1/2,where I is the grain moment of inertia.In the case of suprathermally rotating grains t mech is the time between crossovers,i.e.moments when grain angular velocity approaches zero and the grain?ips over(see Lazarian&Draine1997)5The time between crossovers is approximately the sum of the gaseous damping time t gas and a rather uncertain time of grain resurfacing(see Spitzer&McGlynn1979,Lazarian1995a).When t mech?t L the alignment happens in respect to the direction of gas-grain relative motion. One could expect that in circumstellar regions both situations t mech>t L and t mech

A number of processes can cause the relative grains-gas drift.Stellar winds,out?ows are examples of processes that would tend to align grains with long axis along magnetic ?eld lines.Ambipolar di?usion in Roberge&Hanany(1990)and Alfven waves in Lazarian (1994a)were suggested as the processes that can mechanically align grains perpendicular to magnetic?eld lines.In circumstellar regions and comet atmospheres we expect mechanical alignment to happen mostly along magnetic?eld lines.

2.3.Radiative Torques

The third mechanism that is likely to be dominant in circumstellar regions is based on the action of radiative torques.Although mentioned?rst in Dolginov(1972)and Dolginov &Mytrophanov(1976)this process has not been considered seriously untill very recently. Draine&Weigartner(1996,1997)rediscovered the mechanism and proved using the DDA code that radiative torques(1)can be the dominant source of grain suprathermal rotation

and that(2)these torques can align grains with the longer directions perpendicular to magnetic?eld.The origin of the latter fact is not clear and this tendency contradits to the conclusions in Dolginov&Mytrophanov(1976)6.Nevertheless,treating the properties of radiative torques as established experimentally we have to conclude that this alignment mechanism should be very important in circumstellar regions where the radiation?ux is orders of magnitude higher than that in the interstellar environment.Note,that even in the interstellar medium radiative torques constitue a major mechanism of rotation for

su?ciently large,e.g.a>10?5cm,grains.Within circumstellar regions with enhanced UV?ux smaller grains can be aligned radiatively.This could present a possible solution for the recently discovered anomalies of polarization in the2175?A extinction feature (see Anderson et al1996)that has been interpreted as the evidence of graphite grain alginment(Wol?et al1997).If this alignment happens in the vicinity of particular stars with enhanced UV?ux and having graphite grains in their circumstellar regions,this may explain why no similar e?ect is observed along other lines of sight.

Radiative torques work in unison with paramagnetic relaxation.The situation is less clear when mechanical alignment tends to align grains along magnetic?eld lines, while radiative torques act to align grains perpendicular to magnetic?eld lines.It takes radiative torques at least a few gaseous damping times to align grains7while mechanical alignment can happen in one crossover time.For particular angles between the direction of the incoming radiation and magnetic?eld the grains perform numerous crossovers.This means that in these situations the mechanical alignment should dominate.The theory of crossovers in the presence of radiative torques is being developed(Draine&Lazarian,work in progress)and we hope to learn soon at what conditions the mechanical alignment can win.

3.Polarization

Grain alignment theory can supply R.The observations can get Stocks parameters.To compare observations and the theory one should related R to polarization.Because di?erent de?nitions of R have appeared in the literature and confusing statements have been made in relation to circular polarization of circumstellar origin,we?nd a brief discussion of this subject appropriate.

3.1.Linear Polarization from Aligned Grains

For an ensemble of aligned grains the extinction perpendicular the direction of alignment and parallel to it will be di?erent.Therefore the electromagnetic wave that initially was not polarized acquires polarization.

To characterize the process quantitatively one can consider an electromagnetic wave propagating along the line of sight?z o axis.The transfer equations for the Stokes parameters depend on the cross sections C o x and C o y for linearly polarized waves with the electric vector, E,along the?x o and?y o directions that are in the plane perpendicular to?z o(see Martin 1974,Lee&Draine1985).

To calculate C o x and C o y one transforms the components of E to a frame aligned with the principal axes of the grain and takes the appropriately-weighted sum of the cross sections,C and C⊥,for E polarized along the grain axes.When the transformation is carried out and the resulting expressions are averaged over precession angles,one?nds that the mean cross sections are

1

C o x=C avg+

R C⊥?C ,(6)

3

where C avg≡ 2C⊥+C /3is the e?ective cross section for randomly-oriented grains.

3.2.Circular Polarization from Aligned Grains

One of the ways of obtaining circular polarization is to have magnetic?eld that varies along the line of sight(Martin1972).Passing through one cloud with aligned dust the light becomes partially linearly polirized.On passing the second cloud with dust aligned in a di?erent direction the light gets circular polarized.Literature study shows that this e?ect that is well remembered(see Menard et al1988),while the other process that also creates circular polarization is frequently forgotten.We mean the process of single scattering of light on aligned particles.Electromagnetic wave interacting with a single grain coherently excites dipoles parallel and perpendicular to the grain long axis.In the presence of adsorption these dipoles get phase shift giving rize to circular polarization.This polarization can be observed from the ensemble of grains if the grains are aligned.The intensity of circularly polarized component of radiation emerging via scattering of radiation

with k wavenumber on small(a?λ)spheroidal particles is(Schmidt1972)

I0k4

V(e,e0,e1)=

R([d×r]h)(dr)?Γ(d,r),(8)

6π|d|4|r||d?r|2

where L?is the stellar luminosity,n dust is number density of dust grains andσV

is the cross section for producing circular polarization,which is for small grains is

σV=i/(2k4)(α α?⊥?α?

α⊥).According to Dolginov&Mytrophanov(1978)circular

polarization arising from single scattering on aligned grains can be as high as several percent for metallic or graphite particles,which is much more than one expects from the process of varying magnetic?eld direction along the line of sight.

4.Particular cases

4.1.Circumstellar Regions

Multiple scattering has been used to explain polarization arising from circumstellar regions(see Bastien1988,1996).At the same time it is obvious that in the presence of radiation and magnetic?eld,grains in circumstellar envelops must be aligned perpendicular to magnetic?eld.For the stars that exhibit out?ows and intensive stellar winds,numerical models(see Netzer&Elitzur1994)predict a supersonic relative drift of grain and gas and this should result in mechanical alignment.In circumstellar environments the grain rotation temperature is likely to be much higher than its body temperature.Therefore results for mechanical obtained in Lazarian(1994a)and Lazarian(1995a)are applicable. This entails R～?0.3for both prolate and oblate grains with grain long axis along the out?ow direction.The uncertainty involved,as we have mentioned earlier,is related to the absence of the theory of radiative crossovers.We may claim that our estimate of R is valid for su?ciently small(e.g.a<5×10?6cm)grains,while for larger grains the situation is unclear as yet.

If grains have superparamagnetic or ferromagnetic inclusions and for radiative torques the alignment tends to be nearly perfect(i.e.R～1)with the logner grain dimensions

perpendicular to magnetic?eld lines.If,however,a grain with ferromagnetic inclusions (e.g.“Goodman-Whittet grain”discussed above)is subjected to streaming along?eld lines,it will be aligned perpendicular to magnetic?eld lines as the magnetic relaxation time is typically shorter than that for mechanical alignment.We tend to believe that grain alignment with grain longer axes perpendicular to magnetic?eld and R～1can be a rule for circumstellar regions.Future research should test this conjecture.

The examples above indicate that future modeling of circumstellar regions should include aligned grains.Whether multiple scattering or dichroic adsorption is dominant should be decided by quantitative comparison of the simulations that include both e?ects and observations.Submillimeter polarimetry will be helpful for establishing grain alignment in circumstellar regions(see below).

https://www.doczj.com/doc/9711120380.html,ets

Polarization from comets has been long known to exhibit anomalies(see Martel1960) that motivated a conjecture that grains may be aligned in the comet atmospheres(see Dolginov&Mytrophanov1976).Later studies of linear and circular polarization from Halley and Hale-Bopp comet(Beskrovnaja et al1987,Ganesh et al1998)seem to support this conclusion.

The alignment mechanism operating in comet heads should be really fast.Indeed,dust particles spend only～105s crossing a comet head.Unless magnetic?eld in the comet head is extremely high(e.g.>10?2G)the ferromagnetic relaxation fails to provide the alignment.In comet heads grains are likely to disaggregate and change their shape rather rapidly.This should mitigate the importance of raditative torques that will change their direction with the change of grain shape.At the same time,dramatic changes of grain shapes on the timescale t mech wash out the distinction between prolate and oblate grains and hinder the mechanical alignment as well.

We believe that out?owing gases can be important for grain alignment at the comet head.Calculations in Probstein(1969)indicate that the relative velocities of dust and gas are supersonic.We expect the alignment for thermally rotating grains to be small(e.g.

R～?0.1)and to happen in respect to the out?ow direction.Higher degrees of alignment are possible(e.g.R～?0.3)if grains rotate suprathermally.Indeed,both radiative torques and assymetry in the gas evaporation from grain surface may contribute to suprathermal rotation.Very large dust particles(e.g.a>104cm)may be aligned by a weathercock mechanism discussed in Lazarian(1994b).

Later,in the outer parts of comet coma and in its tail the alignment via radiative torques and interaction with solar wind should be important.R approaching unity is attainable in the former case.Quantitative modeling of the grain alignment in comets is under way(Bastien&Lazarian,work in progress).

4.3.Zodiacal Light

Zodiacal Light,i.e.solar light re?ected from the interplanetary dust particles,is partially polarized.Greenberg(1970)suggested that interplanetary grains could be aligned. Later on similar ideas were discussed by e.g.Wolstencroft&Kemp(1972)and Dolginov& Mytrophanov(1978).

Greenberg(1970)worried that interplanetary particles can be sputtered quicker than be aligned by solar wind.However,his arguments ignore important plasma interactions and ion focusing e?ect(see Draine&Lazarian1998b)that make transfer of angular momentum from solar wind to grains much more e?cient.Thus mechanical alignment is concivable (R～?0.3)with grain long axis along magnetic?eld lines.

The alignment by radiative torques and via ferromagnetic relaxation are possible as well.If large silicate grains that produce most of the linear polarization are aligned along magnetic?eld lines,while a possible population of absorbtive iron grains that would account for most of the circular polarization are aligned perpendicular to interplanetary magnetic ?eld,quite complex picture of polarization may arise.However,it is likely that mechanical alignment is most important for small(a<5×10?6cm)grains,while larger grains are being aligned by radiative torques.Then both small iron grains and large silicate ones are being aligned with long axes perpendicular to the direction of the interplanetary magnetic ?eld.Potentially,studies of Zodiacal Light can bring a lot of information about magnetic ?eld structure and its variability in the Solar neighborhood.

The interplanetary magnetic?eld,as well as those of circumstellar regions and comets, is not stationary.In fact it undergoes variations on a whole range of time scales.If the variations are long compared to the Larmor period t L they are adiabatic in the sence that the angle between grain angular momentum and B is preserved.Therefore time variations of the Zodiacal Light can provide important information on the magnetic variability up to the scale t L.

5.Future Work

It is often di?cult to separate the e?ects of multiple stattering from the e?ects of grain alignment.One of the alluring possibilities is to observe at longer wavelengths, where the e?ects of multiple stattering are negligible.Polarimetry at submillimeter and longer wavelengths should help constructing adequate models of polarized light transfer in circumstellar regions and comets and unrevel magnetic?eld structure in these regions.

Our discussion above was centered on the issue what“classical”or su?ciently large grains can tell us.It looks,however,that very small grains can make a valuable input as well.Recent experiments to map cosmic microwave background,e.g.Kogut et al(1996), Oliveira-Costa et al(1997)and Leitch et al(1997),have revealed a new component of galactic microwave emission at14-90GHz.This component was identi?ed by Draine

&Lazarian(1998a)with the dipole emission from small(a<10?7cm)rotating grains. Lazarian&Draine(1998)predicted that such grains can be aligned and that this should result in anomalous emission being partially polarized.This opens a new valuable window for interstellar and circumstellar studies.An important feature of the relaxation mechanism suggested is that it stays e?cient even when“classical”grains are in thermodynamic equilibrium with the ambient gas and are randomly oriented.Thus the progress in grain alignment theory presents new tools for observers.

6.Conclusions

The principal results of this paper are as follows:

The application of the results obtained in grain alignment theory to comets and circumstellar regions suggest that the dust should be aligned there.Three most important alignment mechanisms are(1)radiative torques,(2)mechanical alignment,(3)ferromagnetic and superparamagnetic relaxation.Observational data supports the conjecture that the dust is aligned in circumstellar regions and comets.Therefore numerical codes that describe radiation transfer in young stellar objects and evolved stars should be modi?ed to account for dust alignment.

The analysis of the images of the dust particles coming from the interplanetary space testify that the ferromagnetic relaxation,rather that superparamagnetic relaxation is likely. The calculated enhancement of the relaxation(compared to that in paramagnetic grains) is～104and is su?ciently large to enable the e?cient alignment of circumstellar dust with ferromagnetic inclusions.

Mechanical alignment and radiative torques compete in aligning grains,(along and perpendicular magnetic?eld lines,respectively)in the regions of out?ows.When streaming velocities are supersonic small grains(a<5×10?6cm)without ferromagnetic inclusions are to be aligned with long axes parallel to magnetic?eld lines,while those with ferromagnetic inclusions are to be aligned with long axes perpendicular to the?eld lines.The situation is still unclear with large(a>10?5cm)grains,but we conjecture that at least in circumstellar regiona and interplanetary space grains are aligned with long axes perpendicular to magnetic?eld.

Both linear and circular polarization provide a valuable input on magnetic?elds in circumstellar regions,comet atmospheres and in the Solar neighborhood.Measurements at submillimeter wavelenghs can disentangle e?ects of multiple scattering from those of grain alignment.In particular cases when large grains are not aligned it is advisable to use microwave polarimetry that is sensitive to the alignment of tiny(a<10?7cm)grains.

Acknowledgements

I am grateful to Pierre Bastien,Bruce Draine,Alyssa Goodman and Peter Martin for helpful discussions and happy to acknowledge the support of NASA grant NAG52858and CITA Senior Research Fellowship.

A.Ferromagnetic and Superparamagnetic Susceptibilities

How superior can be“supergrains”in terms of paramagnetic relaxation?To answer this question we consider iron inclusions.It is well known that small iron particles particles are superparamagnetic(Morrish1980).If iron forms clusters containing N atoms the zero-frequency magnetic susceptibility of a grain increases N times compared with a grain where the same amount of iron is uniformely distributed within a diamagnetic lattice (Draine1996):

χ(0)super≈Nχparam,(A1) where

χparam≈0.04f p n tot5.5 2 15K

How large can be a particle to exhibit superparamagnetic response in oscilating magnetic?eld with frequencyωdepends on the thermally activated relaxation rate

τactiv≈ν0exp[?NT activ/T grain](A3) where T activ≈0.011K andν0≈109s for Fe particles(Bean&Livingston1959).

Forτactivω?1K(ω)super that is equal to the imaginary part ofχ(ω)super/ωis approximatelyχsuperτactiv(Spitzer1978).Whenτactivω>1K(ω)super rapidly decreases with ω(Jones&Spitzer1968,Draine&Lazarian1998c).It is easy to show that the number of iron atoms should not exceed3×103to enable e?cient paramagnetic relaxation of grains rotating faster than105s?1.Therefore the maximal value of K super is approximately 3×103χparamτactiv≈3×10?6χparam.This value should be compared to K param which

is approximately3×10?11χparam(see Draine1996).All in all,the maximal increase of relaxation due to superparamagnetism is given by a factor105.

The latter factor of the relaxation enhancement is frequently quoted in the literature without mentioning that,?rst of all,this is an upper limit for superparamagnetic relaxation enhancement and,even more important,that inclusions of larger size do not exhibit superparamagnetic response forω>105s?1.The minimal number of paramagnetic atoms that make up a superparamagnetic inclusion is uncertain.We know that inclusions with more than20atoms do exhibit superparamagnetism(Billas,Chatelain&de Heer1994). For30atom inclusions the superparamagnetic relaxation is103times enhanced.Inclusions with more than3000atoms will exhibit ferromagnetic properties.

The magnetic susceptibility of large particles follows from the solution of the Bloch equations(see Pake1962)

ω

χ(ω)≈χF e(0)

,(A5)

1+2πχ(ω)

whereχ(ω)is given by Eq.(A4).Therefore for the volume?lling factor of0.01the e?ciency of relaxation for grains with ferromagnetic inclusions is approximately104times that of

a paramagnetic grain.More elaborate calculations show that grains with single domain inclusions exhibit susceptibilities which are a factor5smaller than those found above for the multidomain F e inclusions(Draine&Lazarian1998c).

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what can you do教案(共案)

what can you do教案（共案） 临高三小罗小暖 ( Part A Let’ learn let’ try let’s talk) 教学目标： 1.掌握新词: dance sing English songs do kung fu draw cartoons play the pipa. 2.掌握句型：What can you do? I can… 3.能在实际情景中用所学语言谈论某人是否会做某事。 教学重难点： 1.重点：本课新词、句型。 2.难点：We’ll have…的理解及读音。 情感目标：了解琵琶、武术等具有中国特色的文娱活动， 培养学生的跨文化意识。 学习能力：培养学生的观图猜测能力和小组合作能力。 教学过程： 一．Warm-up and revision. 1.Greeting. 2.I say, you do.

3.Let’s chant: Swim.swim.I can swim. Cook,cook,I can cook. … 二．Presentation 1.Learn the new words and phrases. T:What can you do? S:I can… (学习新词：dance sing English songs do kung fu draw cartoons play the pipa) 2.Practice the new words (1)I say , you do. (2) Let’s chant. What,what,What can you do? Dance,dance,I can dance. … 3.Pre-listening (1)Look and guess: What can Mike do? (2)Listen and tick.

What can you do教学设计

Part B Unit 4 of PEP Primary English Book for Grade Five What can you do? Period 4 教学设计 荆门市东宝区教学研究室廖士新 I Teaching contents（教材分析）: 本课时是PEP Primary English五年级上册第四单元第四课时的内容，课文以图文并茂的形式呈现了五个有关家务劳动的词组、一个交际句型和一段chant。与生活贴近，具有较强的交际性。 II Students analysis（学情分析）： 本课时的教学对象是五年级的学生，他们已经学过两年的英语，有一定的听、说、读、写能力，能就自己喜爱的话题提出相应的问题，能够积极的进行自主学习、合作学习完成学习任务。 III Teaching aims and requirements（教学目标）: 1. Knowledge and abilities（知识技能目标）： 1) 学习有关家务劳动的表达法：wash the clothes, set the table, make the bed，do the dishes，put away the clothes，并能用交际句型“Can you do housework? Yes, I can. I can….”在实际生活情景中熟练地运用。 2) 掌握四会词语：wash the clothes, set the table, make the bed，do the dishes 3) 能吟诵chant。 2. Emotion and tactics（情感态度目标）： 1) 热爱学习，在学习中能集中注意力。 2) 热爱家庭生活，学会做简单的家务劳动。 3. Learning strategy target（学习策略目标）： 同学之间积极合作，共同完成学习任务。 IV Key points and difficult points（教学重难点）: 1. Key points: 掌握四会词语：wash the clothes, set the table, make the bed和do the dishes， 并能在情景中自然的加以运用。 2. Difficult points: 正确拼写四会词语，特别注意指导clothes的发音和拼写。

whatcanyoudo教学设计(李贵元)

《What can you do? A Let’s learn》教学案例与反思 一、教材分析 新人教版小学五年级英语上册Unit4 What can you do ?第二课时,包括Part A的Let’s learn和Do a survey两部分内容，是一节词汇课。主要教学五个动词短语：dance, sing English songs, play the pipa，do kung fu ,draw cartoons.并能运用What can you do? I can...的句型，在实际的教学情景中表述自己会能做的事情及询问别人会做什么。本单元话题的功能是介绍自己在聚会上能做的事情及询问别人能做的事情，与学生日常生活息息相关, 学生特别感兴趣。加之这五个动词短语在以前的学习过程中少数也以出现，它们本身又不难，学生很容易理解。 二、学情分析 五年级学生活泼好动，喜欢直观形象思维和抽象思维相结合，对游戏、表演、竞赛等活动很感兴趣。也已具备了一定的英语基础，初步掌握了运用所学语言进行交际的能力。同时大部分学生对英语有着较浓厚的学习兴趣，但也有少数学生由于遇到困难，学习兴趣会随之减弱。因此，在设计课堂教学活动时我利用媒体出示图片，肢体动作，Flash动画等创设直观的教学情景，采用看、听、说、做、玩、演、唱等灵活多样的教学方法来吸引学生的注意，让他们在丰富多彩、针对性强的活动中来学习英语。努力营造玩中学、学中玩的教学氛围。同时课堂上尽量以鼓励表扬为主，鼓励学生开口说英语、特别是给差生创造机会，让他们尝试成功的喜悦。 三、教学目标： 知识目标： 1、能听、说、读、写：dance, sing English songs, play the pipa，do kung fu ,draw cartoons五个动词短语，并能结合所给句型在实际情景中运用。 2、能够用句型What can you do?询问别人会做什么。并能做出相应的回答。如I can draw cartoons等。 3. 能听懂、会唱歌曲“What Can You Do?”。 能力目标： 1、能在创设的实际情景中灵活运用句型“What can you do?”“I can …”。 2、能在组内完成“Do a survey”部分的对话任务。运用句型“What can you do?”“I can …”询问他人会做的事情。 情感目标： 培养学生小组合作学习，相互沟通和交流的能力。

what about us

歌手：John Barrowman Guess we been talking too long[1] We know what we need Separately... You say the honeymoon's over I don't wanna push But what about us? It's ringing in my head It's not what you say It's what you have said So, What about us? What about love? What about saying That we'll never give up? Don't want to blame ya But we're in danger So... What about us? Guess we been trying too hard We misunderstood What's good for us I'm tired emotionally inside Night after night We fight till we cry I don't know what's wrong or right? Is every word you say What's really on your mind? So... What about us? What about love? What about saying That we'll never give up? Don't want to blame ya But we're in danger So... What about us? When we love... we lie When we talk... we hide Maybe I'm searching blind I'm worn out Confused What are we to you? What do we doing... ? What do we doing? What about us? What about love? What about saying That we'll never give up? Don't want to blame ya But we're in danger So... What about us? What about love? That's the one thing we never discuss Don't want to blame ya But we're in danger So... What about us?

Unit 4 What can you do第一课时教学设计

Unit 4 What can you do第一课时教学设计 Unit 4 what can you do

Unit 4 What can you do第一课时教学设计前言：小泰温馨提醒，英语作为在许多国际组织或者会议上都是必需语言，几乎所有学校 选择英语作为其主要或唯一的外语必修课。英语教学涉及多种专业理论知识，包括语言学、第二语言习得、词汇学、句法学、文体学、语料库理论、认知心理学等内容。本教案根据 英语课程标准的要求和针对教学对象是小学生群体的特点，将教学诸要素有序安排，确定 合适的教学方案的设想和计划、并以启迪发展学生智力为根本目的。便于学习和使用，本 文下载后内容可随意修改调整及打印。 一、教学重点 本课时的教学重点是Let’s learn部分五种家务劳动的表 达方法，要求学生做到四会，并能在情景中自然的加以运用。 二、教学难点 本课时的教学难点是如何利用所提供的对话和情景，以旧引新，让学生进入学习状态。 三、课前准备 1．教师准备教学过程中所需要的图片、英文卡片、声音、 课件。 2．教师准备录音机及录音带。 四、教学过程 1．Warm－up（热身）

（l）Let’s chant ① 教师播放start部分Let’s chant的录音，让学生边听边看图并能理解歌谣的意思。 ② 反复听2-3遍后，可带领学生小声重复。 ③ 拍手掌握节奏，教师将Mike变成本班同学的名字进行提问：Tom, Tom, what can you do？可提问3-4人。 （2）口语练习谁的本领大： ① 男、女生进行比赛，分别用I can…来介绍自己会做的事，看看谁的本领大。 ② 请同学边说边用动作表示，重复不加分，哪组说的最多即为获胜组。 2． Presentation（新课呈现） （l）Start ① 教师出示图片请同学们观看，Oh, so many animals! What can they do? ② 角色扮演：教师提问，Bird, bird, what can you do?请学生挑选自己喜欢的动物边说边做动作。 （2）Let’s learn

what about表示建议

what about表示建议，征求意见,怎么样？ words that you say when you suggest something · I'm thirsty--what about a drink? 我渴了——来一杯，怎么样？ I want a drink.what about you？ 我要来一杯，你呢 how about表示“…怎么样” what do you think of · How about doing it now? 现在来做怎么样？ 一般来讲，应该没有什么大的区别。 I think it is good，how about you？ 我觉得这很好，你觉得怎么样呢 ..

The iron and steel industry is very important to our life. 编辑本段典型例题 The League secretary and monitor ___ asked to make a speech at the meeting. A. is B. was C. are D. were 答案B. 注：先从时态上考虑。这是过去发生的事情应用过去时，先排除A.，C.。本题易误选D，因为The League secretary and monitor 好像是两个人，但仔细辨别， monitor 前没有the，在英语中，当一人兼数职时只在第一个职务前加定冠词。后面的职务用and 相连。这样本题主语为一个人，所以应选B。 2 主谓一致中的靠近原则 1) 当there be 句型的主语是一系列事物时，谓语应与最邻近的主语保持一致。There is a pen, a knife and several books on the desk.. There are twenty boy-students and twenty-three girl-students in the class. 2）当either… or… 与neither… nor，连接两个主语时，谓语动词与最邻近的主语保持一致。如果句子是由here, there引导，而主语又不止一个时，谓语通常也和最邻近的主语一致。 Either you or she is to go. Here is a pen, a few envelopes and some paper for you. 3 谓语动词与前面的主语一致 当主语后面跟有with, together with, like, except, but, no less than, as well as 等词引起的短语时，谓语动词与前面的主语一致。 The teacher together with some students is visiting the factory. He as well as I wants to go boating. 4 .谓语需用单数 1）代词each和由every, some, no, any等构成的复合代词作主语，或主语中含有each, every, 谓语需用单数。 Each of us has a tape-recorder. There is something wrong with my watch. 2）当主语是一本书或一条格言时，谓语动词常用单数。 The Arabian Night is a book known to lovers of English. 《天方夜谭》是英语爱好者熟悉的一本好书。 3）表示金钱，时间，价格或度量衡的复合名词作主语时，通常把这些名词看作一个整体，谓语一般用单数。(用复数也可，意思不变。)

七年级英语下册 Module 2 What can you do教案

Unit 1 I can play the piano. Ⅰ.Teaching Aims: Knowledge aims: 1．能听、说、读、写本单元单词：play, tennis, ride, term, would like, all, that’s all, worry, worry about, teach, then（见课本P104） 2．学生掌握课本P8-9出现的短语和重点句型、情态动词can； Can you…? Yes, I can. / No, I can’t. Which club can…? I can’t…. Ability aims: 学生能够听懂关于参加学校社团等的对话；能够交流各自会干什么与不 会干什么。 Feeling aims: 培养学生认识自我和肯定自我的能力，增强自信心以及助人为乐的精 神。 Ⅱ。Teaching Important Points: 情态动词can 的用法。 Ⅲ. Teaching Difficult points: 情态动词can 的用法。 Ⅳ.Test points: 情态动词can 的用法和零冠词的用法。 【学法指导】仔细阅读课本P92-93关于情态动词can的用法。 一、Self-study(自主学习): 1.自学自读本单元单词（结合词汇表的音标），把不会读的单 词在书上画出来并整理在导学案上。 3．思考：I’d like to join the Music Club because I can play the piano. (英译汉) “can ”是情态动词，在这里，他的意思是。 can没有人称和数的变化，否定式都用cannot（can’t）。详看P92

what about me

Emily Osment - what about me the city is sleepin’ but i’m still awake i’m dreamin’ i’m thinkin’ what happened today is it right? i fall into the night the flashbacks, the pictures, the letters and songs, the memories, the heart that you carved on the wall it’s a shame. now that nothing’s the same now the bridges are burned and we’re lost in the wind it’s time that we sing chorus swell what about you? what about me? what about fairy tale endings? were you just pretending to be? i’m wondering. what if we tried? what if i cried? what if it’s better tomorrow? what if i followed your eyes? i’m wondering, what about me?

you said it. you meant it. you hung up the phone. the talking in circles, it set it in stone. you were gone. we were wrong all along. now the past is the past, and the bruises may fade; these scars are here to stay. what about you? what about me? what about fairy tale endings? were you just pretending to be? i’m wondering. what if we tried? what if i cried? what if it’s better tomorrow? what if i followed your eyes? i’m wondering, what about me? stay away you stayed away i’m not afraid anymore what about you? what about me? what about fairy tale endings? were you just pretending to be? i’m wondering.

what can you do 精品公开课教案

人教版PEP 小学英语五年级上册 Unit4 What Can You Do ？第二课时教学设计 1.整体设计思路、指导依据说明优化教学活动设计，发挥活动设计的最大功效。紧密联系学生的生活实际，体现语言的交际功能，贯彻语言运用的基本原则，把知识和技能目标融会在完成任务的过程中，从而体现了教材提出的把话题——功能——结构——任务结合起来的总思路。根据学生的年龄特点，精心设计教学活动，让学生在有节奏的说唱、游戏中体验语言，在有韵律的歌唱中感受语言，在轻松愉快的行动中输入语言，让他们在做中学，在唱中学，在表演中学（Learning English by doing/singing/acting…）从而为培养他们用英语进行顺利的交流打下坚实的基础。 2.教学背景分析教学内容分析：（注：含本课时在本单元的教学定位分析）能够听、说、认读句:Are you helpful at home Sure.What can you do I can....Great You’re helpful.让学生更好的掌握和运用“做家务”这个主题的语言项目，并学会调查对方能干什么以及回答，让全班学生能“动”起来，“活”起来，并促进了学生的发展。 3.教学目标分析: （一）知识目标 1、通过自主学习与小组合作探究，能够听懂、会说、并能准确翻译： Are you helpful at home ? What can you do ? I can sweep the floor. You’re helpful ! 2、通过创设情境，通过小组合作练习，能够询问别人能做什么:What can you do ?会用I can….进行回答。 3、关心父母，树立热爱劳动，体贴父母的观念。 （二）能力目标 1、能简单介绍自己能做哪些家务劳动，如：I can clean the bedroom. I can cook the meals. 2、能询问别人能做什么家务劳动，如：What can you do? 3、能运用在实际中运用教材中的句型。 （三）情感、策略、文化目标 1、情感态度：养成讲究卫生、热爱劳动的好习惯，懂得为社会贡献自己力量， 培养乐于助人的优秀品质。 2、学习策略：注重小组合作学习，培养相互沟通和交通的能力。 4.教学重点、难点分析教学重点、教学难点：句子“Are you helpful at home ”以及在实际情景中正确运用所学对话。 5.教学过程设计 步骤 1：Warm up （2 分钟） 1、Greeting. 设计意图：（分四大动物组:dog，

What短语用法小结

What用法小结 一,what about与how about 用这两个短语放在句首的简略问句,都可以用来表示征求意见或询问情况.两者可以互换,但有时不能,what about也有别的用法和解释.例如:What about going to Harbin tomorrow =How about going to Harbin tomorrow What about the funding Where are we going to get it =How about the funding Where are we going to get it 注意what about有别的用法和解释.例如: What about it =What shall we do What about the others(Concerning the others, what is your plan or idea 别的人怎么办(至于别人,人有什么打算或意见) What about it (Tell me more precisely what you mean.) 这是怎么回事(把你的意思明确的地告诉我.) 二,what if, what of和what for 这三个短语的用法和含义各不相同.What if表示"倘若……将会怎样即使……又有什么关系呢";what of 表示"……的情况怎样……又有什么重要性呢;what for为何目的为什么.例如: What if it rains while we are out 倘若我们外出遇上下雨,那怎么办呢 What of it 那有什么了不起呢(那又怎么样呢) Well, and what of it (It has no importance.) 嗯,那又怎么样呢(怎么,那有什么了不起) What for did you ask that silly question Now he's going to speak for another ten minutes. 你干吗要问那个愚蠢的问题这一来他又得说上十分钟. What did you do that for 三,what作the thing that 或as much…as解. What作关系代词,其作用相当于the thing或people that,请比较: =This is just the book that I have been looking forward to. The thing that I like most in her is her kindness. =What I like most in her is her kindness. The upstart is not what he was ten years ago. =The upstart is not the man that was ten years ago. 这个暴发户已经不是十年前那个人了. 四,What作关系形容词,其作用相当于as much…as, whatever.请比较: She will give the sick baby what care she can. =She will give the sick baby as much care as she can. Lend me what money you have on hand. 五,What …is或What…are 当what引导的从句作主语时,谓语动词要根据表语的内容判断.请比较: What I need most are two books. What I need most is only one book. 六,what is+形容词或副词比较级 常用的短语有:what is more而且;what was worse 更糟糕的是;what is better而且更可贵的是;what is the best of all最难能可贵的是,what is more important更重点的是;what is more

whatcanyoudo教案

Unit 4 what can you do? 课题第四单元第一课时 课型新授时间 学习目标 1. 能听、说、读、写单词“sing”，“song”，“kung fu”，“dance”和词组“sing English songs”，“play the pipa”，“do kung fu”，“draw cartoons”。 2. 能在创设的实际情景中灵活运用句型“What can you do?”，“I can …”。 3. 能听懂、会唱歌曲“What can you do?”。 4. 能完成“Do a survey”部分的对话任务。 5. 鼓励学生了解身边同学的能力，做生活中的有心人。 学习重难点 1. 能听、说、读、写单词“sing”，“song”，“kung fu”，“dance”和词组“sing English songs”，“play the pipa”，“do kung fu”，“draw cartoons”。 2. 能在创设的实际情景中灵活运用句型“What can you do?”，“I can …”。教学难点 1. 新词汇和词组的学习。 2. 能在创设的实际情景中灵活运用句型“What can you do?”，“I can …”。教学过程二次备课 一、课前热身（Warm-up） 1. Free talk T: Good morning, everyone. Welcome back to school. How are you today? Ss: Fine, thank you. And you? T: I’m fine, too. Are you ready for our class? Ss: Yes. 2. 热身活动 T: Now let’s do some warming-up practice. All of you, listen to me, please. Stand up and follow me. Run, I can run (read, jump, swim, fly, clean, draw …). 二、课前预习（Preview） 学习歌曲“What can you do?” T: You can jump, run, swim … You’re so great. Now let’s learn a song ca lled “What can you do?”. 第一次播放歌曲录音，全班学生跟着录音唱歌曲。 第二次播放歌曲录音，全班学生分男女比赛唱歌曲。 三、新课呈现（Presentation） 1. A. Let’s learn (1) 学习新单词和词组。 创设“考艺校”情景：“明星艺校”来学校招生啦！很多学生报名参加考试，让我们来看看同学们都表演些什么才艺吧！ 教师用课件依次出示跳舞、唱英文歌曲、弹琵琶、练功夫和画漫画的情景，引出新单词和词组，并将其写在黑板上。 dance sing English song play the pipa do kung fu draw cartoons (2) 教师带领学生读几遍新单词和词组，然后让学生分组读、分男女生读。

what用法面面观

what用法面面观 夏金彪 在高考英语中，考查或涉及what一词用法的试题频频出现，只把它对译成汉语的“什么”是不够的。现将其用法归纳如下： 一. what 作疑问代词，意为“什么；哪个，哪些”。在句中作主语、宾语、表语或定语。例如： What happened to him？（主语）他发生了什么事？ What did you say？（宾语）你说什么？ Now what is this？（表语）那么这是什么？ What colour are your curtains? （定语）你的窗帘是什么颜色的？ What country do you come from？（定语）你来自哪个国家？ 有时what前面可以带上介词。例如： For what did you do it？（=What did you do it for？）你为何做这件事？ On what will you depend？（=What will you depend on？）你将依靠什么？ By what means did they get the information？他们是用什么方法得到这个信息的？ In what circumstances will they sign the treaty？他们将在什么情况下签订条约？ At what time did he finished the work？他在什么时间完成这项工作的？ 二. what 用作关系代词，相当于the thing (s) that / which ；the place that / which；the person that / who，引导名词性从句，what 在从句中也充当句子成分。例如： What she saw （= The thing that she saw ）gave her a fright. （引导主语从句） 她看到的情况吓了她一跳。 I want to tell you what I hear. （引导宾语从句）我想告诉你我听到的。 He isn’t what he used to be. (引导表语从句) 他不是以前的他了。 I lived in what (= the place that) you call ancient Greece. （引导宾语从句）我生活在你们称之为古希腊的地方。 There arose the question what you did last night？（引导同位语从句）这就产生一个问题：你昨天晚上做什么了？ 三. what 引导感叹句。例如： What a good heart you have! 你的心肠真好！ What bad weather it is! 多糟糕的天气呀！ What nonsense you talk! 你说什么糊涂话！ 感叹句的主语、谓语有时可省略。例如： Oh, What a beautiful picture! 噢，多漂亮的一幅画！ 四. what 用于固定结构中。 1. what about 表建议或征求对方意见，意为“……怎么样？”。例如： Of course I'll come. What about Friday? 我当然要来，星期五怎么样？ What about sending him a copy? 送他一本怎么样？

英语疑问词的用法

英语疑问词的用法 疑问代词：what 什么, which 哪一个, who 谁, whom 谁, whose谁的 疑问副词：when 什么时间，where 什么地方，why 为什么，how 怎么样 疑问形容词：what（which，whose）+名词 一、what 什么用来问是什么，叫什么，做什么等 1. What’s your name? 你叫什么名字？ 2.What is in your box? 你的盒子里是什么？ 3. What’s your father?=What does your father do? 你爸爸是干什么的？ 一）what time 什么时间用来问点时间 What time is it? 几点了？ 二）what colour什么颜色用来问颜色 What colour is your bag? 你的书包是什么颜色？ 三）what about 怎么样用来征求意见或询问感受等,大多用于承接上面的同样问题。 1.Whatabout this pair of shoes? 这双鞋子怎么样？ 2.What about you? 你呢？ 四）what day 星期几用来问星期几 What day is it today/tomorrow? 今天/明天星期几？ 五）what date 什么日期问具体的日期 What’s the date today? 今天是几号？What date is tomorrow? 明天是几号？ 二、when 什么时候用来问时间 When do you get up?你什么时候起床？ 三、where 哪里用来问地点 1. Where is my ruler? 我的尺子在哪里？ 2. Where are you going? 你打算去哪里？ 3.Where are you from? =Where do you come from? 你是哪里人？ 四、which 哪一个用来问具体的哪一个 1. Which season do you like best? 你最喜欢哪个季节？ 2.Which class are you in? 你在哪一个班？ 3.Which one is my pen？哪一支是我的钢笔？ 五、who 谁用来问人物是谁 1.Who is that boy?那个男孩是谁？ 2. Who are you going to go with? 你打算和谁一起去？ 3. Who is that pretty lady?那个漂亮的女士是谁？ 4. Who teaches you English?谁教你们英语？ 六、whose 谁的用来问东西是谁的 1. Whose bag is this? 这是谁的包？ 2.Whose bike is yellow? 谁的自行车是黄色的？ 七、why 为什么用来问原因 1.Why do you like spring? 你为什么喜欢春天？ 2. Why did you go there? 你为什么去那里？ 八、how 怎么样用来问方式或者询问身体等状况 1. How are you? 你好吗？ 2. How is your mother? 你妈妈好吗？ 3. How did you come here? 你们是怎么来的？ 4. How did they finish the work so quickly?他们是如何这么快完成工作的？ 一）How old 几岁用来问年龄How old are you? 你几岁了？ 二）How long 多长(1) 用来问时间How long does the film last? 这部电影放多长时间？ （2）用来问长度How long is the bridge? 这座桥有多长？ 三）How big 多大用来问物体的大小How big is your bedroom? 你的卧室多大？ 四）How tall 多高用来问高度How tall is your brother? 你弟弟有多高？ 五）How far 多远用来问路程How far is it from here? 从这儿去有多远？ 六）How many 多少用来问可数名词的数量How many apples do you have? 你有多少苹果？七）How much （1）多少用来问不可数名词的数量

What can you do教案

《What can you do?》教案 新天学区刘平 教学内容： Pep版小学五年级上册Unit4《What can you do?》Part A 教学目标： 1、能力目标： a、让学生使用What can you do? I can …这两个句型。 b、并让学生掌握表示做家务的五个短语，从而让他们在生活中使用英语进行交流。 2、知识目标： a、掌握五个表示家务劳动的短语：wash the windows、cook the meals、water the flowers、sweep the floor 、clean the bedroom b、学会使用What can you do? I can …并运用此句型进行日常交流。 3、情感目标： a．教育学生热爱劳动、多做家务，为父母亲做一些力所能及的事情。 b．同学之间互相帮助，善于与人相处。 c．做一个对社会、对家庭有用的人。 d．培养学生自我评价的能能力。 教学重点： 1、wash the windows、cook the meals、water the flowers、sweep the floor 、clean the bedroom五种家务劳动的表达方法。 2、让学生使用What can you do? I can …这两个句型，并让学生掌握表示做家务的五个短语。 3、生活中使用英语和老师、同学、亲人进行交流，实现英语课程的最

终目标：培养学生综合语言运用的能力。 教学难点： 运用所学的英语知识，在生活中进行英语交流。 教学过程 一、热身导入： 1、教师播放英语歌曲colour song。 2、反复听2-3遍后，可带领学生轻声跟唱。 3、拍手掌握节奏，师生一起用手打节拍演唱英语歌曲colour song来集中学生的注意力。 二、新知； （1）Presentation（新课呈现） 老师：Boys and girls，do you like this song？ 学生：Yes. 老师：What do you do on Sundays? 学生：I often do my homework ,watch TV and do housework. 老师: Who can tell us what can you do at home？ 老师: What can you do? 学生：我能浇花、扫地、做饭、打扫卧室…I can…（sweep the floor、cook the meals、 clean the bedroom、 water the flowers、wash the windows）老师: Oh! You are helpful. Today we are going to learn some new phrases with screen. （2）Let’s learn 1、老师布置任务，出示Let’s learn 的图片问：What can you do? 2、学生在小组内自学五个词组，然后再分别找学生来教学五个短语，让学生

whatabout和howabout的用法

What about和How about的用法 What about … 和how about … 是英语口语中常用的两个省略句型，它们的意思和用法基本相同，常常用在以下场合。例如：一、向对方提出建议或请求。例如： 1．How about going out for a walk 出去散散步好吗 2．What about another cake 再吃块蛋糕好吗 二、征询对方的看法或意见。例如： 1、What about the playing the violin （你认为）她的小提琴拉的怎么样 2、What about the TV play 那个电视剧怎么样 三、询问天气或身体等情况。例如： 1、What about the weather in your home town 你们家乡的气候如何 2、How about your uncle now You can’t leave him by himself. 你叔叔近来身体好吗你们不能单独让他生活。 四、寒暄时用作承接上下文的转折语。例如： I am from Beijing. What about you 我是北京人，你呢 五、对所陈述的情况做出反诘，常给予对方一种暗示。例如： ——My memory is good. I’ve never forgotten anything.我的记忆力很好，从不忘记什么。——What about that time you left your key to the office at home那次你将办公室的要是忘在家里算是怎么回事呀 Agree的用法（） agree是一个使用范围很广的单词，意为“同意；赞同”。它有很多相关词组，现在把其主要用法归纳如下： 1. agree (to sth) 意为“同意；愿意；答应（某事物）”。如：Is he going to agree to our suggestion 他会同意我们的建议吗 2. agree with sb 意为“适合（某人的健康或胃口）”，尤用于否定句或疑问句中。如：The climate there doesn\'t agree with him. 那里的气候对他不合适。 3. agree (with sb) (about / on sth) 意为“同意；（与某人）意见一致”。如：We couldn\'t agree on a date/ when to meet. 关于日期（什么时候见面），我们没有能取得一致意见。 4. agree sth意为“在某事物上取得一致意见；商定”。如：Can we agree a price 我们能不能商定一个价格 5. agree (with sth) 意为“与（某事物）相一致；相符合；相吻合”。如：Your thoughts didn\'t agree with mine. 你的想法和我的想法不一致。 6. be agreed（on /about sth）意为“达成协议；意见一致”。如：We are all agreed on the best action. 我们都同意这一最佳措施。 7. agree后面还可以接宾语从句，即be agreed that ...如：It was agreed that another