Impurity and boundary effects in one and two-dimensional inhomogeneous Heisenberg antiferro

a r X i v :c o n d -m a t /0412554v 1 [c o n d -m a t .s t r -e l ] 20 D e c 2004Impurity and boundary e?ects in one and two-dimensional inhomogeneous Heisenberg

antiferromagnets

P.E.G.Assis,Valter L.L′?bero and K.Capelle

Departamento de F′?sica e Inform′a tica,Instituto de F′?sica de S?a o Carlos,Universidade de S?a o Paulo,

Caixa Postal 369,13560-970S?a o Carlos,SP,Brazil

(Dated:February 2,2008)

We calculate the ground-state energy of one and two-dimensional spatially inhomogeneous anti-

ferromagnetic Heisenberg models for spins 1/2,1,3/2and 2.Our calculations become possible as

a consequence of the recent formulation of density-functional theory for Heisenberg models.The

method is similar to spin-density-functional theory,but employs a local-density-type approximation

designed speci?cally for the Heisenberg model,allowing us to explore parameter regimes that are

hard to access by traditional methods,and to consider complications that are important speci?cally

for nanomagnetic devices,such as the e?ects of impurities,?nite-size,and boundary geometry,in

chains,ladders,and higher-dimensional systems.

PACS numbers:71.15.Mb,75.10.Jm,75.50.Ee

The study of low-dimensional spin systems is one of the central issues in the physics of correlated electrons.Model Hamiltonians of the Heisenberg type are widely used to study,e.g.,antiferromagnetically coupled spin chains,ladders,and layers,1,2and constitute most use-ful models for strong correlations in undoped cuprates and manganites.Finite-size Heisenberg models,more-over,serve as paradigmatic models for the emerging ?eld of nanomagnetism and spintronics.However,progress in the analysis of nanomagnetic devices requires capability to deal with ‘real-life’complications,such as impurities of arbitrary size and location,boundaries of various shapes,and crossovers between ?nite and extended systems,or between one and higher dimensions.In the present paper we present a convenient and e?cient numerical approach for calculating ground-state energies of antiferromagnetic Heisenberg models subjected to such complications.Traditional numerical methods are well suited for studying generic properties of homogeneous Heisenberg models,and have provided many important insights into the physics of magnetic systems.However,the very sig-ni?cant expenditure of computational e?ort required by methods such as group-theory-aided exact diagonaliza-tion,Quantum Monte Carlo (QMC),3or the density-matrix renormalization group (DMRG),4imposes rather strict limits on the size and complexity of systems that can be studied.The mean-?eld approximation can,in principle,be applied to systems of almost arbitrary size and complexity,but its neglect of correlation makes it un-reliable as a tool for studying many issues of current phys-

ical interest in strongly correlated systems.In ab initio

calculations,density-functional theory (DFT)provides a

convenient and reliable way to go beyond the mean-?eld

(Hartree)approximation,allowing to study real systems

of considerable size and complexity.5,6,7While DFT is

in principle an exact reformulation of the many-body

problem,8its practical implementation requires the use

of approximations for the exchange-correlation energy.

Among the most important such approximations is the

local-density approximation (LDA),the essence of which is to use the exchange-correlation energy of the uniform electron liquid locally as an approximation to the one of the crystal or molecule of interest.5,8The formal frame-work of DFT and the LDA is not limited to the ab initio case,but can be applied to a large class of model Hamil-tonians,too.9,10,11,12,13In the present paper we study the ground-state en-ergy of one and two-dimensional antiferromagnetic sys-tems with broken translational symmetry,as a function of spin S and system size N .Our choice of symmetry-breaking terms is dictated by complications expected to arise in real nanomagnetic devices,and includes bound-aries of diverse geometries,and di?erent types of impuri-ties.Our calculations are performed within DFT for the Heisenberg model,?H =J ij ?S i ·?S j + i B i ·?S i ,(1)where B i is a symmetry-breaking magnetic ?eld,cou-pled to the spins.The simplest local-spin approxima-tion (LSA)for the correlation energy of Hamiltonian (1)reads 12E LSA c,d =1[S i ]=?0.36338J i |S i |(2)in one dimension,and E LSA c,d =2[S i ]=?0.316J i |S i |(3)in two dimensions.More sophisticated approximations are discussed in Ref.12.Here |S i |is the modulus of the classical vector S i ,the ground-state expectation value of the local spin operator ?S i .The total-energy functional then takes the form E [S i ]=J i,j S i ·S j +E LSA c [S i ]+ i B i ·S i ,(4)where the ?rst term on the right-hand side is the mean-?eld result,the second the LSA correlation correction to

2 it,and the last describes the coupling to(possibly spa-

tially varying)magnetic?elds.Below we set B i=0

because we will mostly be interested in intrinsic inho-

mogeneities such as surfaces and impurities,but both

LSA functionals can be applied for nonzero B i=0as

well.Minimization of E[S i]with respect to S i yields the

ground-state energy E0.Minimization of the?rst(mean-

?eld)term on its own results in the familiar antiferromag-

netic N′e el state with alternating up and down spins.For

open boundary conditions14in one dimension this state

has energy E MF

0,d=1

(S)=?JS2(N?1),while for a two

dimensional square lattice E MF

0,d=2(S)=?2JS2N(N?1),

where N is the number of sites along the chain and along

one side of the square,respectively.E LSA

c provides an

additive correction to E MF

.

First,we consider?nite size Heisenberg chains.In Fig.1we compare,separately for each spin,the ground-state energies obtained in the mean-?eld approximation, in LSA,and by exact diagonalization.To be able to compare with exact results we have limited us to fairly small systems,but clearly mean-?eld and LSA calcula-tions can be performed easily for much larger systems. The LSA is seen to provide substantial improvement on the mean-?eld results,at negligible extra computational cost.However,we also observe that the LSA does not reproduce the oscillatory structure in the exact results visible for small N,but instead smoothly interpolates through it.As expected on physical grounds,12the LSA becomes better as the system size increases.

In these calculations the system is inhomogeneous only due to its?nite size.However,the LSA concept can also be applied to spin Hamiltonians in which translational symmetry is broken more radically.Speci?cally,we now consider an impurity model of much current physical in-terest:an impurity of spin S I in a magnetic host ma-terial of spin S.This type of model is relevant,e.g., for the analysis of impurities in the antiferromagnetic parent compounds of cuprate superconductors,1impu-rities in correlated spin chains,15and recent proposals for quantum computing.16,17Fig.2shows the ground-state energy of a spin1/2antiferromagnetic Heisenberg chain,with open boundary conditions,in which one of the boundary spins has been replaced by a spin1ion, as schematically indicated in the inset.Mean-?eld,LSA, and exact values are given.The exact data show that for this type of impurity system the improvement on the mean-?eld approximation provided by the LSA is of the same order as in the homogeneous case studied in Fig.1. For comparison purposes we have also included the LSA predictions for an impurity in the bulk,and for a sys-tem with two impurities,one in the bulk and one at the surface.Clearly,an antiferromagnetically coupled bulk impurity with S I>S is energetically more favorable than a surface one,suggesting that self-assembled nano-magnetic systems with this type of impurity will tend to accumulate the impurities in the bulk,and leave the surface homogeneous.The ratio of the energy di?erence between bulk and surface impurities to temperature is the controlling parameter for studies of impurity migra-tion.We?nd that this parameter depends strongly on the impurity spin S I and system geometry.The extra computational e?ort for applying the LSA is small,and does not increase signi?cantly if more than one impurity is present,thus opening the possibility to model realis-tic nanomagnetic systems,with hundreds or thousands of sites,with LSA.

Next,we consider an antiferromagnetic background of spin S=1/2and varying size,with an impurity of spin S I>S at the surface.Fig.3shows how the combined system background+impurity approaches the thermody-namic limit for each value of spin S I.The lowest curve, representing the uniform system,approaches the ther-modynamic limit from below,and converges to it rather rapidly.The upper three curves represent the behaviour for di?erent sizes of the impurity spin.The impurity curves approach the thermodynamic limit from above,at a rate that—due to the spin-dependence of the prefac-tors of the overall1/N decay—decreases with increasing impurity spin.Physically,this behaviour can be under-stood by noting that for small N the impurity greatly increases the energy of the model as compared to the uni-form case,while,as the system size approaches in?nity, the in?uence of the impurity localized at the boundary becomes negligible,and all curves converge to the value E0/JN=?0.432,close to the value E0/JN=?0.443 obtained from the Bethe Ansatz for the uniform system. Next,we turn to the two-dimensional case.Here exact diagonalization becomes prohibitively expensive at even smaller system sizes than in one dimension,and alterna-tive methods,such as DMRG,also encounter very signif-icant di?culties.In Fig.4we plot the LSA ground-state energy of?nite-size two-dimensional Heisenberg models. These are calculations without impurities,so that the in-homogeneity arises only from the presence of the system boundary,which breaks translational invariance.(As in one dimension,impurities of arbitrary size and location can be added to these systems without a signi?cant in-crease in computational cost.)Given the LSA functional (3),the generation of the LSA data is a very simple ex-tension of the mean-?eld calculation.In spite of its sim-plicity,however,this calculation illustrates an important aspect of LSA:it has the same margin of error in higher dimensions as in one.This is rather untypical of many-body methods,which usually work better in certain di-mensionalities(often d=1)than in others.

Finally,we investigate an e?ect that does not exist in one dimension,namely the dependence of the ground-state energy on the geometry of the system.In Table I we compare the ground-state energies of?ve Heisenberg models with100sites,of shape1×100,2×50,5×20, 10×10and2×5×10.These systems represent,re-spectively,a one-dimensional chain of the type studied in Fig.1,a spin ladder with constant coupling along legs and rungs,a multi-legged ladder,a square lattice of the type investigated in Fig.4,and a representative three-dimensional structure.The data show that:(i)for larger

3

spins the e?ect of the system boundary becomes more pronounced.This may be relevant for the study of quan-tum corrals,19and di?erently shaped magnetic quantum dots.(ii)The higher-dimensional the system,the slower is the convergence to the thermodynamic limit:our result for the100site spin1/2chain di?ers only by3%from the thermodynamical limit obtained from the Bethe-Ansatz, whereas with the same number of spins the energy of the10×10square lattice is about9%from the thermo-dynamical limit reported in Ref.20;a deviation of3% from this limit is obtained only for a50×50lattice.(iii) The step from a chain to a two-legged ladder is much bigger than that from a two-legged ladder to a square lattice,suggesting that in terms of their ground-state energy even small ladders are more similar to extended two-dimensional systems than to chains.(iv)Compari-son of the columns1×100and1×100(2d)shows that simple extrapolation of a higher-dimensional functional to lower dimensionalities results in less negative energies than the correct functional.This observation may also be relevant for ab initio calculations applying LDA to low-dimensional systems.

In summary,our results show that the Heisenberg LSA is quantitatively reliable,goes signi?cantly beyond the mean-?eld approximation,and allows to calculate the energy of systems of considerable size and complexity. Similar results can be obtained with QMC,3but at orders of magnitude higher computational cost.(Unlike QMC, DFT is also not limited by a minus-sign problem.)QMC, DMRG and exact data provide benchmarks for testing the quality of improved density functionals.On the other hand,LSA data on the e?ects of the boundary geome-try,the energetic in?uence of impurities of di?erent sizes and locations,the approach to the thermodynamic limit, and e?ects of increased dimensionality may be useful in-formation for analysing real nanoscale antiferromagnetic systems,and can also serve as a guide for the application of alternative many-body methods to the same type of system.

Acknowledgments

This work was supported by FAPESP and CNPq.We thank F.C.Alcaraz and A.Malvezzi for useful discus-sions.

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N.Gidopoulos and S.Wilson,(Kluwer Academic Publish-ers,2003)[also available as cond-mat0209245].

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14For space reasons we report here only results for open boundary conditions,but all our calculations can be per-formed for periodic boundary conditions,too.

15M.Kenzelmann,G.Xu,I. A.Zaliznyak, C.Broholm, J.F.DiTusa,G.Aeppli,T.Ito,K.Oka,and H.Takagi, Phys.Rev.Lett.90,087202(2003).16A.H.Castro Neto,E.Novais,L.Borda,G.Zarand and

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18For S=1/2the benchmark values for N<22were obtained by us,by exact numerical diagonalization.For N=24and32they were taken from Ref.21;for N=8 and N≥16they coincide with those from Ref.22.For S=1the benchmark values for N<15were obtained by us,by exact diagonalization.For S=3/2and S=2the benchmark values are estimates extracted from Fig.1of Ref.23.

19H.C.Manoharan,C.P.Lutz,and D.M.Eigler,Nature 403,512(2000).

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4

FIG.1:Ground-state energy of the?nite antiferromagnetic Heisenberg chain for various values of the spin S.For each spin,the diamonds represent the mean-?eld results,the cir-cles are numerically precise benchmark values obtained in in-dependent many-body calculations,18the full line is obtained with LSA,and the dashed horizontal line represents the value obtained in the thermodynamic limit,taken from Ref.4.The LSA is seem to provide signi?cant improvement on the mean-?eld values,for all S and N.

FIG.2:Ground-state energy of an antiferromagnetic S=1/2 Heisenberg chain with an S I=1impurity at the surface. Horizontal line:mean-?eld result.Dashed curve:LSA result. Circles:exact values,obtained by numerical diagonalization. Full curve:LSA result for same system,but with the impurity in the bulk.Dash-dotted curve:LSA results for same system, but with two impurities.FIG.3:Ground-state energy of an antiferromagnetic S=1/2 Heisenberg chain with di?erent impurities S i at the bound-ary.Mean-?eld values are not included because from Fig.2 we see that they are much inferior to LSA ones for this sys-tem.Crosses:homogeneous system.Diamonds:impurity spin S I=1,open circles:impurity spin S I=3/2,full cir-cles:impurity spin S I=2.The arrow indicates the exact Bethe-Ansatz result E0/NJ=?0.443147.

FIG.4:Ground-state energy of?nite antiferromagnetic Heisenberg square lattices,as a function of spin and system size.Here N stands for the number of sites along the side of the square,hence the total number of sites is N2.Dashed curves:mean-?eld(MF)results.Full curves:LSA results. Full circles:benchmark data obtained by exact diagonaliza-tion of small clusters.Arrow:N→∞limit,from Ref.20.

5 TABLE I:Ground-state energy?E0/100J of antiferromag-

netic Heisenberg models of?xed size N=100,and varying

geometries and dimensionalities.For each dimensionality we

used the proper functional,12except in the column labeled

1×100(2d),which contains values obtained for the1d system

with the2d functional(see discussion in main text).

S1×1001×100(2d)2×505×2010×102×5×10

3579

1113151719

0.20.3

0.4

0.5

0.6mean?field (surface)

Fig.2

exact (surface)?E 0/N J N LSA (surface)

S I = 1

LSA (bulk)LSA (bulk+surface)

...

510152025

3035404550

0.30.4

0.5

0.6

0.7

0.8

+?E 0/N J ?N S I ?Fig.3

23/211/2. . .

101000

2

4

68N ?E 0/N 2J MF LSA S=1/2

S=1

S=3/2S=2Fig.4exact

?

英语介词口诀

英语介词用法口诀 早、午、晚要用in，at黎明、午夜、点与分。 年、月、年月、季节、周，阳光、灯、影、衣、冒in。 将来时态in...以后，小处at大处in。 有形with无形by，语言、单位、材料in。 特征、方面与方式，心情成语惯用in。 介词at和to表方向，攻击、位置、恶、善分。 日子、日期、年月日，星期加上早、午、晚， 收音、农场、值日on，关于、基础、靠、著论。 着、罢、出售、偷、公、假，故意、支付、相反，准。 特定时日和"一……就"，on后常接动名词。 年、月、日加早、午、晚，of之前on代in。 步行、驴、马、玩笑on，cab，carriage则用in。 at山脚、门口、在当前，速、温、日落、价、核心。 工具、和、同随with，具有、独立、就、原因。 就……来说宾译主，对、有、方状、表细分。 海、陆、空、车、偶、被by，单数、人类know to man。 this、that、tomorrow，yesterday，next、last、one。 接年、月、季、星期、周，介词省略已习惯。 over、under正上下，above、below则不然， 若与数量词连用，混合使用亦无关。' beyond超出、无、不能，against靠着，对与反。 besides，except分内外，among之内along沿。 同类比较except，加for异类记心间。 原状because of,、owing to、due to表语形容词 under后接修、建中，of、from物、化分。 before、after表一点, ago、later表一段。 before能接完成时，ago过去极有限。 since以来during间，since时态多变换。 与之相比beside，除了last but one。 复不定for、找、价、原，对、给、段、去、为、作、赞。 快到、对、向towards，工、学、军、城、北、上、南。 but for否定用虚拟，复合介词待后言。 ing型由于鉴，除了除外与包合。 之后、关于、在......方面，有关介词须记全。 in内to外表位置，山、水、国界to在前。

英语介词用法大全

英语介词用法大全 TTA standardization office【TTA 5AB- TTAK 08- TTA 2C】

介词（The Preposition）又叫做前置词，通常置于名词之前。它是一种虚词，不需要重读，在句中不单独作任何句子成分，只表示其后的名词或相当于名词的词语与其他句子成分的关系。中国学生在使用英语进行书面或口头表达时，往往会出现遗漏介词或误用介词的错误，因此各类考试语法的结构部分均有这方面的测试内容。 1. 介词的种类 英语中最常用的介词，按照不同的分类标准可分为以下几类： (1). 简单介词、复合介词和短语介词 ①.简单介词是指单一介词。如： at , in ,of ,by , about , for, from , except , since, near, with 等。②. 复合介词是指由两个简单介词组成的介词。如： Inside, outside , onto, into , throughout, without , as to as for , unpon, except for 等。 ③. 短语介词是指由短语构成的介词。如： In front of , by means o f, on behalf of, in spite of , by way of , in favor of , in regard to 等。 (2). 按词义分类 {1} 表地点（包括动向）的介词。如： About ,above, across, after, along , among, around , at, before, behind, below, beneath, beside, between , beyond ,by, down, from, in, into , near, off, on, over, through, throught, to, towards,, under, up, unpon, with, within , without 等。 {2} 表时间的介词。如： About, after, around , as , at, before , behind , between , by, during, for, from, in, into, of, on, over, past, since, through, throughout, till(until) , to, towards , within 等。 {3} 表除去的介词。如： beside , but, except等。 {4} 表比较的介词。如： As, like, above, over等。 {5} 表反对的介词。如： againt ,with 等。 {6} 表原因、目的的介词。如： for, with, from 等。 {7} 表结果的介词。如： to, with , without 等。 {8} 表手段、方式的介词。如： by, in ,with 等。 {9} 表所属的介词。如： of , with 等。 {10} 表条件的介词。如：

表示地点的介词

表示地点的介词 in、on、behind、next to、near、over、under (1) in在……里面：The pencil is in the desk. 铅笔在课桌里。 (2) on在……上面：There are some apple on the tree. 树上有些苹果。 (3) under在……下面/正下方：What's under your desk? 你书桌底下是什么？ (4) over在……正上方：There is a shelf over the table. 桌子上方有一个书架。 (5) above 在……斜上方：Raise your arms above your head. (6) below 在……斜下方：Her skirt came below her knees. (7) behind在……之后：There is a bike behind the tree. 树后有一辆自行车。 (8) next to在……旁边：There is a shop next to the school. 理发店隔壁是一家咖啡馆。 (9) near在……附近：My bed is near the window. 我的床在窗户旁。 (10) by在……旁：He was sitting by the window. (11) beside 在旁边He sits down beside Jim. 一组：over, above和on的用法 1) over指在…的正上方，表示垂直在上。如 There is a lamp over the desk. 2) above指在上方，属于斜上方。如： Raise your arms above your head. 3) on指在上面，表示两物体接触。如： There is a cup on the table. 二组：under / below的用法： 1) under在……下面/正下方： What's under your desk? 2) below 在……斜下方： Her skirt came below her knees 三组：in 和on表示“在……上” 1)门/窗一类——镶嵌在墙里的，用in; 2)字画一类——挂/贴在墙面上的，用on ( ) 1 He put up a map ___ the back wall because there was a hole ______ it. A. on; on B. at; in C. on; in D. on; at ( ) 2 There is a door___ the wall. A. on B. to C. of D.in 3)人/鸟其他东西在树上，用in; 4)枝叶果实长在树上的，用on ( ) 1 There are some birds singing___ the trees. A. in B. on C. at D. from ( ) 2 There are so many apples___ that tree. A.in B, on C of D.from

介词in,on.at,for.with,by,of的基本用法

介词用法知多少 介词是英语中最活跃的词类之一。同一个汉语词汇在英语中可译成不同的英语介词。例如汉语中的“用”可译成：（1）用英语（in English）；（2）用小刀（with a knife）；（3）用手工（by hand）；（4）用墨水（in ink）等。所以，千万不要以为记住介词的一两种意思就掌握了这个介词的用法，其实介词的用法非常广泛，搭配能力很强，越是常用的介词，其含义越多。下面就简单介绍几组近义介词的用法及其搭配方法。 一. in, to, on和off在方位名词前的区别 1. in表示A地在B地范围之内。如： Taiwan is in the southeast of China. 2. to表示A地在B地范围之外，即二者之间有距离间隔。如： Japan lies to the east of China. 3. on表示A地与B地接壤、毗邻。如： North Korea is on the east of China. 4. off表示“离……一些距离或离……不远的海上”。如： They arrived at a house off the main road. New Zealand lies off the eastern coast of Australia. 二. at, in, on, by和through在表示时间上的区别 1. at指时间表示： （1）时间的一点、时刻等。如： They came home at sunrise （at noon, at midnight, at ten o’clock, at daybreak, at dawn）. （2）较短暂的一段时间。可指某个节日或被认为是一年中标志大事的日子。如： He went home at Christmas （at New Year, at the Spring Festival, at night）. 2. in指时间表示： （1）在某个较长的时间（如世纪、朝代、年、月、季节以及泛指的上午、下午或傍晚等）内。如： in 2004, in March, in spring, in the morning, in the evening, etc （2）在一段时间之后。一般情况下，用于将来时，谓语动词为瞬间动词，意为“在……以后”。如： He will arrive in two hours. 谓语动词为延续性动词时，in意为“在……以内”。如： These products will be produced in a month. 注意：after用于将来时间也指一段时间之后，但其后的时间是“一点”，而不是“一段”。如： He will arrive after two o’clock. 3. on指时间表示： （1）具体的时日和一个特定的时间，如某日、某节日、星期几等。如： On Christmas Day（On May 4th）, there will be a celebration. （2）在某个特定的早晨、下午或晚上。如： He arrived at 10 o’clock on the night of the 5th. （3）准时，按时。如： If the train should be on time, I should reach home before dark. 4. by指时间表示： （1）不迟于，在（某时）前。如：

介词用法口诀

介词用法口诀： 早、牛、晚要用in at黎明、午夜、点与分 年、月、年月、季节、周，阳光、灯、影、衣、帽in 将来时态in表以后，小处at大处in 有形with无形by 语言、单位、材展in 早、午、晚要用in in the morning 在早上 in the afternoon 在下午 in the evening 在晚上 in the day在白天 at黎明、午、夜、点与分 at dawn, at daybreak^ 黎明时候 at noon在中午at night在夜间 at midnight 在午夜 at six o'clock 在6 点钟 at 7:30 （seven thirty）在7 点半 at the weeken血周末 年、月、年月、季节、周都用in in 1986 在1986 年 in March在三月 in July, 1983 1983 年7 月i n spring在春季 in the third week 在第三周 阳光、灯、影（树荫）、衣、冒（雨）in Don't read in dim light.切勿在暗淡的灯光下看书。 They are sitting in the shade of a tree.他们坐在树阴下乘凉。 He went in the rain to meet me at the station. 他冒雨到车站去接我。 the woman in white （black, red, yellow）穿着白（黑、红、黄）色衣服的妇女in uniform 穿着制服 将来时态in表以后 They will come back in 10 days 他们将10 天以后回来。

介词的用法

（一）介词概述 介词是一种虚词，在句子中不单独作任何句子成分。它是一种表示名词和句中其他词之间关系的词。它常和名词、动词、形容词等搭配，构成固定短语，表示不同意思。介词还可以与名词构成介词短语，表示方位、方向、时间、地点、方式、原因等。这些介词短语在句中可充当定语、状语、补语等。2000—2005年的中考中主要考了形容词与介词的搭配：如：be famous for；表示时间的介词，如：at night；动词与介词的搭配，如：arrive in/have dinner with sb.；表示方式、手段的介词，如：by phone/in English. （二）基础知识梳理 1．名词与介词的搭配 a bit of有一点儿 a couple of两个、几个 a kind of一种、一类cover an area of占地面积 have pity on sb.怜悯某人huge amounts of大量的 make friends with与……交朋友make fun of拿……开玩笑 meet the needs of迎合……的需要one after another一个接一个；连续地 play a trick on捉弄the week after next下下周 2．动词与介词的搭配 agree with sb.同意某人的意见apologize to sb. for sth.为某事向某人道歉arrive at/in a place到达某地ask for请求、寻求 be covered with被……所覆盖be made of由……制成 be made up of由……组成belong to属于 break into破门而人、闯入 call on拜访 care for照顾、喜欢carry out执行 check in办理登机come across被理解；遇见 come from出生于、来自come on跟我来、走吧

地点和位置的介词

表示地点和位置的介词 1.at, in, on 1) at 表示较狭窄较小的地方（小村庄，小城镇），in 表示较大的地方（大城市，大的空间）。 I met her at the bus-stop. They arrived at the famous town in South Jiangsu. She is living in Nanjing. There are a great many islands in the Pacific. 2) 门牌号码前用at，road前面用on，street前用in或on。 in the street (BrE) on the street (AmE) at 103 Wall Street on the road 3) 把某个机构看成是机关或组织时用at，看成一个具体的地方时用in She is at Oxford. 她在牛津读书。She is in Oxford 她在牛津居住（工作或逗留） 4）at可以表示有意、有目的的行为。 She is at the table. 她在吃饭She is beside/ by the desk. 她坐在桌旁。 5) on 在---上面，表示上下两者紧贴在一起，in 表示在---里面。 She put the book on the desk. She put the book in the desk. She wore a smile on her face. (面部表情) She was wounded in the face. （伤有深度） 2．on 和underneath underneath 是on的反义词，表示某物紧贴在另一物的底下 There is a piece of paper underneath the dictionary. 3.under 和over under 和over 是一对反义词，表示正上方，正下方，没有接触的含义。 There are some chairs under the tree. The lamp hung over the table. under 和over 还可以表示上级、下级。 He is over us= We are under him. 4. above 和below 两者是一对反义词，表示高于、低于，既不表示接触，也不表示上下垂直。 The plane is flying above us. The sun has sunk below the horizon. 5. beneath 可以和underneath, under, below 互换。 6．at, by, beside at 表示有目的的接近、接触，by和beside 表示偶然的接近，不接触。 She will be waiting for you at the school gate at 7 tomorrow. The girl stood by/ beside her mother. To those who stand by me, I shall stand by my promise. 对那些支持我的人，我将恪守诺言。 7．near 和next to Near 表示在---附近，靠近；next to 表示紧挨着，紧靠着。 No birds or animals came near the lake. She went and sat next to him. 8. before, in front of, at the front of, ahead of before 用于某人前；in front of 用于建筑物前；in front of 和ahead of 用于空间可互换，用于时间只能用ahead of；in the front of 表示内部空间的前部；at the front of 表示外部空间

英语中表示时间、地点和位置的常用介词的应用 (自动保存的)

英语中表示时间、地点和位置的常用介词的应用 内容摘要：介词是一种用来表示词与词, 词与句之间的关系的词,在句中不能单独作句子成分。介词后面一般有名词代词或相当于名词的其他词类、短语或从句作它的宾语。介词在英语中有非常重要的地位,但其种类繁多,用法复杂,一个介词还往往有多种意义,本文将从时间、地点和用名词尤其是由动词转化过来的名词的机会较多,而名词与名词之间常常需要介词连接,故英语中使用介词的现象比比皆是。 关键词:表示时间地点和位置附加状语名词动词 内容： 一、英语中表示时间的常用介词 after表示...之后，指某事发生在所指时间后的任意时间，是before的反义词，表示在...之后（1）用在附加状语里，常跟有-ing小句，，如： Li Ming was released from prison after serving three years.李明在服刑三年后出狱。（2）用在名词之后，如：I hate the time after sunset before you come home.我不喜欢日落之后、你回家之前的这段时间。（3）用在动词be之后，如：He turned and went after his brothers.他转身去追赶他的兄弟们。after通常指次序的先后。 in（1）表示在某世纪、年、季度、月、周”以及泛指的上、下午、晚上。如：in the 20th century在20世纪；in 1999在1999年；in winter在冬季；in September在九月；in the morning/afternoon/evening 在上午/下午/晚上。（2）in 过...后(未来时间)，不晚于，如：The train will arrive in three hours.火车三小时到。（3）表示某段时间之后，如：to return in a few minutes/hours/days/months几分钟/几小时/几天/几个月后回来。（4）表示做...时，...发生时，当...时，如：In attempting to save the child from drowning, she nearly lost her own life.她在抢救落水儿童时，自己差点丧命。 注：after与in都可表示“在……之后”，但after后可跟时间段，也可跟时间点；而in后必须跟时间段。after既可用于将来时，也可用于过去时，而in只能用于将来时。I’ll arrive in an hour. 我一小时后到。 during表示在……期间(1)某事在某段时间里连续发生或发生过几次，用在附加状语里，如：During all the years of work, he had been realistic with himself.这些年来在所有的工作中，他总是对自己实事求是。（2）表示某物在某段时间里从开始到结束，都一直得到发展，用在附加状语里，如:I hope this will become clear to you during the course of the lectures.我希望在讲座过程中，你会渐渐明白这一点。（3）指某事在某一期间内的某一刻发生，用在附加状语里，如：The boy disappeared from the hotel during the night.这名男孩在夜间从旅馆失踪。 from表示时间的起点，从……起，多用于“from…to/till…”中。如：You can come anytime from Monday to Friday. 周一至周五你什么时间来都行。from 仅说明什么时候开始，不说明某动作或情况持续多久。 for 表示达...之久（1）过了多少时间，后接“一段时间”，表示某事持续多久，多与完成时连用，如：She has been ill for several days. 她已经病了几天了。（2）表示某事已经发生过一次，用在附加状语里，如：Before using a pan for the first time, wash it with a sponge.在首次使用平底锅前，用

英语介词的用法总结

介词的用法 1.表示地点位置的介词 1)at ,in, on, to，for at (1)表示在小地方; (2)表示“在……附近，旁边” in (1)表示在大地方; (2)表示“在…范围之内”。 on 表示毗邻，接壤，“在……上面”。 to 表示在……范围外，不强调是否接壤；或“到……” 2)above, over, on 在……上 above 指在……上方,不强调是否垂直，与below相对； over指垂直的上方,与under相对,但over与物体有一定的空间，不直接接触。 on表示某物体上面并与之接触。 The bird is flying above my head. There is a bridge over the river. He put his watch on the desk. 3)below, under 在……下面 under表示在…正下方 below表示在……下，不一定在正下方 There is a cat under the table. Please write your name below the line. 4)in front [frant]of, in the front of在……前面 in front of…意思是“在……前面”，指甲物在乙物之前，两者互不包括；其反义词是behind（在……的后面）。There are some flowers in front of the house.(房子前面有些花卉。) in the front of 意思是“在…..的前部”，即甲物在乙物的内部.反义词是at the back of…（在……范围内的后部）。 There is a blackboard in the front of our classroom. 我们的教室前边有一块黑板。 Our teacher stands in the front of the classroom. 我们的老师站在教室前.(老师在教室里) 5）beside，behind beside 表示在……旁边 behind 表示在……后面 2.表示时间的介词 1)in , on，at 在……时 in表示较长时间，如世纪、朝代、时代、年、季节、月及一般（非特指）的早、中、晚等。 如in the 20th century, in the 1950s, in 1989, in summer, in January, in the morning, in one’s life , in one’s thirties等。 on表示具体某一天及其早、中、晚。 如on May 1st, on Monday, on New Year’s Day, on a cold night in January, on a fine morning, on Sunday afternoon等。 at表示某一时刻或较短暂的时间，或泛指圣诞节，复活节等。 如at 3:20, at this time of year, at the beginning of, at the end of …, at the age of …, at Christmas，at night, at noon, at this moment等。 注意：在last, next, this, that, some, every 等词之前一律不用介词。如：We meet every day. 2)in, after 在……之后 “in +段时间”表示将来的一段时间以后； “after+段时间”表示过去的一段时间以后； “after+将来的时间点”表示将来的某一时刻以后。 3)from, since 自从…… from仅说明什么时候开始，不说明某动作或情况持续多久；

英语地点介词的正确使用方法

英语地点介词的正确使用方法 地点介词主要有at ，in，on，to，above，over，below，under，beside，behind ，between。它们的用法具体如下： 1、at （1）at通常指小地方：In the afternoon，he finally arrived at home。到下午他终于到家了。 （2）at通常所指范围不太明显，表示“在……附近，旁边”：The ball is at the corner。球搁在角落里。 2、in （1）in通常指大地方：When I was young，I lived in Beijing。我小时候住在北京。 （2）在内部：There is a ball in in the box。盒子里有只球。 （3）表示“在…范围之内”（是从属关系）： Guangdong lies in the south of China。深圳在中国的南部。 3、on

（1）on主要指“在……之上”，强调和表面接触： There is a book on the table。桌上有一本书。 （2）表示毗邻，接壤（是相邻关系）： Canada lies on the north of America 加拿大在美国的北边（与美国接壤）。 4、to 主要表示“在……范围外”，强调不接壤，不相邻。 Japan is to the east of China。日本在中国的东面。 注意： （1）at 强调“点”，on 强调“面”，in 强调“在里面”，to 表示“范围外”。 （2）on the tree：表示树上本身所长着的叶子、花、果实等 in the tree：表示某物或某人在树上 on the wall：表示在墙的表面，如图画、黑板等 in the wall：表示在墙的内部中，如门窗、钉子、洞、孔 5、above

表示地点位置的介词

表示地点位置的介词 w qsa 1)at ,in, on, to，for at (1)表示在小地方; (2)表示“在……附近，旁边”in (1)表示在大地方; (2)表示“在…范围之内”。on 表示毗邻，接壤，“在……上面”。to 表示在……范围外，不强调是否接壤；或“到……”2)above, over, on 在……上above 指在……上方,不强调是否垂直，与below相对；over指垂直的上方,与under 相对,但over与物体有一定的空间，不直接接触。on表示某物体上面并与之接触。The bird is flying above my head. There is a bridge over the river. He put his watch on the desk. 3)below, under 在……下面under表示在…正下方below表示在……下，不一定在正下方There is a cat under the table. Please write your name below the line. 4)in front [frant]of, in the front of在……前面in front of…意思是“在……前面”，指甲物在乙物之前，两者互不包括；其反义词是behind（在……的后面）。There are some flowers in front of the house.(房子前面有些花卉。) in the front of 意思是“在…..的前部”，即甲物在乙物的内部.反义词是at the back of…（在……范围内的后部）。There is a blackboard in the front of our classroom. 我们的教室前边有一块黑板。Our teacher stands in the front of the classroom. 我们的老师站在教室前.(老师在教室里) 5）beside，behind beside 表示在……旁边behind 表示在……后面 2.表示时间的介词 1)in , on，at 在……时in表示较长时间，如世纪、朝代、时代、年、季节、月及一般（非特指）的早、中、晚等。如in the 20th century, in the 1950s, in 1989, in summer, in January, in the morning, in one’s life , in one’s thirties等。on表示具体某一天及其早、中、晚。如on May 1st, on Monday, on New Year’s Day, on a cold night in January, on a fine morning, on Sunday afternoon等。at表示某一时刻或较短暂的时间，或泛指圣诞节，复活节等。如at 3:20, at this time of year, at the beginning of, at the end of …, at the age of …, at Christmas，at night, at noon, at this moment等。注意：在last, next, this, that, some, every 等词之前一律不用介词。如：We meet every day. 2)in, after 在……之后“in +段时间”表示将来的一段时间以后；“after+段时间”表示过去的一段时间以后；“after+将来的时间点”表示将来的某一时刻以后。3)from, since 自从……from 仅说明什么时候开始，不说明某动作或情况持续多久；since表示某动作或情况持续至说话时刻，通常与完成时连用。since表示"自（某具体时间）以来"，常用作完成时态谓语的时间状语。since liberation（1980）自从解放（1980年）以来They have been close friends since childhood．他们从小就是好朋友。（1）since the war是指"自从战争结束以来"，若指"自从战争开始以来"，须说"since the beginning of the war"。（2）不要将since与after混淆。比较：He has worked here since 1965．（指一段时间，强调时间段）自从1965年以来，他一直在这儿工作。He began to work here after 1965．（指一点时间，强调时间点）从1965年以后，他开始在这儿工作。4)after, behind 在……之后after主要用于表示时间；behind主要用于表示位置。时间名词前介词用法口诀年前周前要用in 具体日子要用on 遇到几号也用on 上午下午得是in 要说某日上下午用on换in记清楚午夜黄昏用at 黎明用它也不错at用在时分前说“差”可要用上to 说"过''要用past 3.表示运动方向的介词： across, through 通过，穿过across表示横过,即从物体表面通过，与on有关，为二

介词的用法及习题

第七单元介词 我们经常在名词或名词短语、代词或动名词前用介词表示人物、事件等与其它句子成分的关系。介词后面的名词或相当于名词的词语叫介词宾语。介词可表示地点、时间、比较、反对、原因、手段、所属、条件、让步、关于、对于、根据等。 二、介词的意义 1．表示时间的介词 in表示“在某一时间段”，或“在……某一时候”，如用在月、季、年份、时代、世纪等时间名词的前面，或用来泛指一天的某一段时间。 In July/summer/2000/ancient times/the 1999’s In the morning/afternoon/evening In也可以指“在……之后”，表示从说话起的若干时间内，如： The bus will be here in ten minutes. On表示“在特定的某一天”，也可用于带有修饰语的一天的某个时间段之前。如： on Saturday, on Saturday morning, on the morning of August 1st at表示“在某一时间点”，或用来表示不确定的时间和短期的假日、时节等。如： at six o’clock, at Easter 介词over, through (out)两者均指“经过的全部时间”。 Stay over the Christmas. 介词for, since for表示动作或状态延续的全部时间长度，为“长达……”之意；since用于指从过去特定的某个时刻到说话时为止的一段时间；两者往往用于完成时。 I have been there for six years. We have not seen each other since 1993. During指“在……时期/时间内”，必须以表示一段时间的词或词组作宾语。 She was ill for a week, and during that week she ate little. 2．表示地点的介词 介词at指小地点或集会场合；on表示线或面上的位置；in表示在立体、区域或环境内，特别是那些教大，能够容纳相应事物的环境。 He works at Peking University. Your radio is on the desk. The boat is in the lake. 3．表示原因的介词 for常常表示褒贬、奖惩的原因或心理原因。 4．表示目的的介词 for表示拟定的接收人或目的；to表示实际的接收人或目的。 I bought the gift for my little sister. I gave the gift to my little sister. 5．表示“关于……”的介词 一般about用于比较随便的谈话或非正式的文体；on用于正式的讲话、著作或报告中；7．表示价格的介词 at和for都可表示价格，at仅表示价格，for还表示“交换”，如： Eggs are sold at 95 cents a dozen here. I bought it for five pounds.

时间地点介词的用法

具体日期前用“on” 注意: 一、含有this, that, these, those, every, each 等的时间状语前不用介词。如： We are going to play football this afternoon. 今天下午我们打算踢足球。 His father goes to work early every day. 他爸爸每天很早去上班。They are working on the farm at the moment. 这几天他们正在农场干活。 二、all day, all week, all year 等由“all +表示时间的名词”构成的时间状语前不用介词。如： We stay at home and watch TV all day.我们整天呆在家里看电视。 三、由“some, any, one等＋表示时间的名词”构成的时间状语前不用介词。如： We can go to the Great Wall some day. 有一天我们会去长城的。 四、时间状语是today, tomorrow, tomorrow morning, tomorrow afternoon, tomorrow evening, the day after tomorrow (后天)等，其前不用介词。如：

What day is it today?今天星期几？ Who's on duty tomorrow? 明天谁值日？ MORE: at 表示时间的某一点 （节日或年龄、瞬间或短暂的时间） Your memory is always poor at this time. （表示一天中的某个时刻不用冠词） I got up at six in the mopning. on 表示某日或和某日连用的某个时间段 You were late on Monday last week. in 用于表示除日以外的某一时间段 （表示年、月、季节、世纪时代） Sorry, I am late, the frist time in May. in和at都可表示地点，而in表示的地点比at所表示的地点大

英语表示地点位置的介词

表示地点位置的介词 1)at ,in, on, to at (1)表示在小地方; (2)表示“在……附近，旁边”in (1)表示在大地方; (2)表示“在…范围之内”。on 表示毗邻，接壤，“在……上面”。 to 表示在……范围外，不强调是否接壤；或“到……” 2)above, over, on 在……上 above 指在……上方,不强调是否垂直，与below相对； over指垂直的上方,与under相对,但over与物体有一定的空间，不直接接触。 on表示某物体上面并与之接触。 The bird is flying above my head. There is a bridge over the river. He put his watch on the desk. 3)below, under 在……下面 under表示在…正下方 below表示在……下，不一定在正下方 There is a cat under the table. Please write your name below the line. 4)in front of, in the front of在……前面 in front of…意思是“在……前面”，指甲物在乙物之前，两者互不包括；其反义词是behind （在……的后面）。 There are some flowers in front of the house.(房子前面有些花卉。) in the front of 意思是“在…..的前部”，即甲物在乙物的内部.反义词是at the back of…（在……范围内的后部）。There is a blackboard in the front of our classroom. 我们的教室前边有一块黑板。Our teacher stands in the front of the classroom. 我们的老师站在教室前.(老师在教室里) 5）beside，behind beside 表示在……旁边 behind 表示在……后面 2.表示时间的介词 1)in , on，at 在……时 in表示较长时间，如世纪、朝代、时代、年、季节、月及一般（非特指）的早、中、晚等。 如in the 20th century, in the 1950s, in 1989, in summer, in January, in the morning, in one’s life , in one’s thirties等。 on表示具体某一天及其早、中、晚。 如on May 1st, on Monday, on New Year’s Day, on a cold night in January, on a fine morning, on Sunday afternoon等。 at表示某一时刻或较短暂的时间，或泛指圣诞节，复活节等。如at 3:20, at this time of year, at the beginning of, at the end of …, at the age

时间名词前介词用法口诀

英语中按动词后可否直接跟宾语，可以把动词分成两种：及物动词与不及物动词。及物动词：字典里词后标有vt. 的就是及物动词。及物动词后必须跟有动作的 对象（即宾语），并且可直接跟宾语。 如see 看见 (vt.) +宾语 I can see a boy. 不及物动词：字典里词后标有vi. 的就是不及物动词。不及物动词后不能直接 跟有动作的对象（即宾语）。若要跟宾语，必须先在其后添加上某个介词，如 to,of ,at后方可跟上宾语。具体每个动词后究竟加什么介词就得联系动词短语了，如listen to,look at…. 如：look 看 (vi.) x宾语(即不能直接加宾语). Look! She is singing. Look carefully! (注意：carefully 是副词，不是名词，故不作宾语) look at 看…….+宾语 Look at me carefully! (me是代词，作宾语) 介词是一种用来表示词与词, 词与句之间的关系的虚词。在句中不能单独作句子成分。介词后面一般有名词代词或相当于名词的其他词类，短语或从句作它的宾语。介词和它的宾语构成介词词组，在句中作状语，表语，补语或介词宾语。并且在定语从句“介词+whom/which”的结构中，不能用that 代替who/which。She is a good student from who we should learn. 介词分为时间介词.地点位置方向介词.方式介词.原因介词和其他介词，是英 语中最活跃的词类之一，特别是一些常用介词的搭配力特别强，可以用来表示各种不同的意思。英语里大部分习语都是由介词和其他词构成的。介词在句中一般不重读\ 表示地点位置的介词 1)at ,in, on, to，for at (1)表示在小地方; (2)表示“在……附近，旁边” in (1)表示在大地方; (2)表示“在…范围之内”。 on 表示毗邻，接壤，“在……上面”。 to 表示在……范围外，不强调是否接壤；或“到……” 2)above, over, on 在……上 above 指在……上方,不强调是否垂直，与 below相对； over指垂直的上方,与under相对,但over与物体有一定的空间，不直接接触。 on表示某物体上面并与之接触。 The bird is flying above my head. There is a bridge over the river. He put his watch on the desk. 3)below, under 在……下面 under表示在…正下方 below表示在……下，不一定在正下方 There is a cat under the table. Please write your name below the line.