a r X i v :c o n d -m a t /0412584v 1 [c o n d -m a t .o t h e r ] 21 D e c 2004
Ab initio many-body calculation of excitons in solid Ne and Ar
S.Galami′c -Mulaomerovi′c and C.H.Patterson
Department of Physics and Centre for Scienti?c Computation,University of Dublin,Trinity College,Dublin 2,Ireland
(Dated:February 2,2008)
Absorption spectra,exciton energy levels and wave functions for solid Ne and Ar have been calculated from ?rst principles using many-body techniques.Electronic band structures of Ne and Ar were calculated using the GW approximation.Exciton states were calculated by diagonalizing an exciton Hamiltonian derived from the particle-hole Green function,whose equation of motion is the Bethe-Salpeter equation.Singlet and triplet exciton series up to n =5for Ne and n =3for Ar were obtained.Binding energies and longitudinal-transverse splittings of n =1excitons are in excellent agreement with experiment.Plots of correlated electron-hole wave functions show that the electron-hole complex is delocalised over roughly 7a.u.in solid Ar.
PACS numbers:71.10.Li,71.35.-y,71.35.Aa,78.40.-q
I.INTRODUCTION
Electronic and optical properties of rare gas solids (RGS)Ne and Ar have been studied experimentally 1,2,3,4,5,6,7,8,9,10and theoretically 11,12,13,14,15,16,17,18and have been the subject of several review articles 19,20,21.Optical absorption spectra are characterized by sharp exciton peaks at energies up to sev-eral eV below the fundamental band gap.Excitons in RGS consist of a hole in a p -type valence band and an electron in an s -type conduction band.The momentum of the hole can be either j =3/2(spin triplet)or j =1/2(spin sin-glet).Spin-orbit coupling mixes these states and so pairs of transverse exciton lines,labelled by principal exciton quan-tum numbers n and n ′,are observed in optical absorption ex-periments.When spin-orbit coupling is weak,as in Ne,ener-gies of these excitons ought to be close to the spin singlet and triplet energies.Creation of longitudinal excitons in electron energy loss experiments produces a longitudinal polarisation ?eld which couples to the associated long-range macroscopic electric ?eld and leads to energy splitting of longitudinal (L)and transverse (T)excitons of the same principal quantum number.
An integral equation approach has been applied to excitons in insulators for over 40years 22.This incorporates screened electron-hole attraction and exciton exchange terms in the Hamiltonian.Early applications of this approach to RGS 12,13used an approximation in which the exciton wavefunction was restricted to a single unit cell (one site approximation).Following this,Resca and coworkers developed an approach which took into account the delocalised nature of the exci-ton wavefunction by solving an effective mass equation 14,15,18.In this approach the electron-hole attraction term was un-screened when both electron and hole were on a single site and screened by a macroscopic dielectric constant factor when they were on different sites.Modi?cation of the electron-hole attraction term as a function of electron-hole separation in this way leads naturally to a quantum defect correction,E n =E g ?B ex /(n +δn )2,to the Wannier formula for ex-citon energies,E n =E g ?B ex /n 2.E g is the fundamen-tal band gap and B ex is the exciton binding energy.Resca and Resta 15showed that the former expression could predict exciton energies rather well with a weak dependence of the
quantum defect,δn ,on n.However,subsequent direct mea-surements of the fundamental band gaps in RGS 23showed that the fundamental gap derived from a ?t to the Wannier formula (excluding the n ′=1exciton)yielded a value for E g in good agreement with the experimental values while the quantum defect model yielded quite different values.Bern-storff et al.24concluded that RGS excitons ’do not possess atomic parentage’.Exciton wavefunctions for RGS are there-fore well known to have strong but incomplete localization of the electron and hole on the same site.This intermedi-ate binding character of excitons in RGS means that they are far from the well-separated electron-hole pair limit,which applies to semiconductors and is well described by the ef-fective mass approximation theory 25.A recent calculation 11,which used a screened Coulomb electron-hole interaction and a Slater-Koster parametrization of the band structure,found good agreement with experimental exciton energies and delo-calization of the electron-hole wavefunction over three nearest neighbor distances.
The integral equation approach was applied to diamond 26,27and silicon 28by Hanke and Sham in the 1970’s using a tight-binding parameterization of the band structure.Strinati 29showed how the equation of motion for the particle-hole Green function,the Bethe-Salpeter equation 30,for core-hole excitons could be reduced to an effective eigenvalue prob-lem.Recent ab initio calculations of valence excitons in crys-talline solids 31,32,33have been based on this effective eigen-value problem and the Bethe-Salpeter formalism has been reviewed 34.In this paper we present ab initio calculations of excitonic absorption spectra and correlated electron-hole wave functions for excitons in Ne and Ar.Quasiparticle band energies are calculated using the GW approximation 35and the Bethe-Salpeter formalism 34,which includes statically screened electron-hole attraction and exciton exchange terms,is used to calculate the optical spectrum.This is generated us-ing matrix elements between the ground state and correlated electron-hole excited states and the longitudinal-transverse (LT)splitting of excitons is investigated.
The remainder of the paper is arranged as follows:In Sec-tion II the theoretical formalism is presented,in Section III re-sults of calculations of optical spectra and correlated electron-hole wave functions in solid Ne and Ar are given and ?nally
2 conclusions are given in Section IV.
II.THEORETICAL BACKGROUND
A.Quasiparticle energies
The starting point in our approach is to generate the quasi-
particle energies and wave functions of the system.Quasi-
particle energies are obtained by solving the quasiparticle
equation36,
H(r)ψQP
m
(r)+ Σ(r,r′,E)ψQP m(r′)d r′=?mψQP m(r),(1)
using perturbation theory.The unperturbed Hamiltonian is a
Kohn-Sham Hamiltonian and the self-energy operator,Σ,is
obtained using the GW approximation(GW A).Quasiparti-
cle wave functions,ψQP
m (r),are approximated by eigenfunc-
tions of the unperturbed Kohn-Sham Hamiltonian.Density functional theory(DFT)within the Perdew-Wang generalized gradient approximation37(PWGGA)is used to obtain DFT eigenvectors and eigenvalues.Details of GW calculations as well as quasiparticle band structures along symmetry lines for Ar and Ne are given in Ref.[35].The CRYSTAL code38 was used to generate single-particle wave functions for Ne and Ar in an all-electron Gaussian orbital basis and the Coulomb potential was expanded in plane waves.GW and BSE cal-culations were carried out using the EXCITON39code.The spin-orbit interaction was omitted from the calculations and experimental lattice constants were used19.
B.Electron-hole excitations and optical spectra Correlated electron-hole states,|N,S ,can be represented in a basis of single-particle quasi-electron(conduction,c)and quasi-hole(valence,v)states,
|N,S = k vc A S k vc?a??b?|N,0 = k vc A S k vc|k vc ,(2) where?a?and?b?create a quasi-hole and quasi-electron,re-spectively,in the many-body ground state|N,0 .Coupling
coef?cients,A S
k vc ,and excitation energies,?S,are obtained
by solving the BSE in the form34,
(E k c?E k v)A S k vc+ k′v′c′ vc k|Ξ|v′c′k′ A S k′v′c′=?S A S k vc,(3) whereΞdenotes the electron-hole interaction and energies E k c and E k v are quasiparticle energies obtained within the GW A.The interaction kernel,Ξ,is given as a sum of two terms34:the screened electron-hole attraction,also called the direct interaction,Ξd,and the exchange interaction,Ξx,which results from bare Coulomb repulsion.Neglecting any dynami-cal screening,the matrix element of the direct term in a plane-wave basis is given by,
vc k|Ξd|v′c′k′ =?
4πe2
|q+G||q+G′|× v′k′|e?(q+G)·r|v k c k|e??(q+G′)·r|c′k′ δq,k′?k.(4)
ε?1
GG′
(q,ω=0)is the symmetrized,inverted,static RPA di-electric matrix40,G and G′span the reciprocal lattice and?denotes the crystal volume.When computing the matrix el-ements in Eq.(4)special care has to be taken for the case q→0.If G=G′=0the interaction diverges as1/q2.This contribution is separated from the left side of Eq.(3)and in-tegrated over a small sphere of volume V=V BZ/N k where V BZ is the volume of the Brillouin zone and N k is the num-ber of k points,as suggested by Arnaud and Alouani33.This divergence contributes notably only when v=v′and c=c′. In addition a divergence of type1/q occurs when one of the G vectors is zero.These terms are neglected,because their contribution either averages to zero or vanishes in the limit of a large number of k points33.
The exchange term of the interaction for singlet states has the form34,
vc k|Ξx|v′c′k′ =
2×
4πe2
G2
c k|e?G·r|v k v′k′|e??G·r|c′k′ .(5)
The G=0term omitted from Eq.(5)is responsible for LT splitting of singlet excitons41.It has the form,
2×
4πe2
E k c?E k v
.?Q?Q T.
v′k′|p|c′k′
?q2 S|
v,c,k v k|e??q·r|c k A S k vc|2
3 In Eq.(7)optical transitions are given as a coherent sum
of the transition matrix elements of the contributing electron-
hole pair con?gurations,including the coupling coef?cients,
A S k vc.Without the electron-hole interaction,excitations are
given by vertical transitions between independent electron and
hole states.In that limit Eq.(7)reduces to the well known
RPA dielectric function,
εRP A M (ω)=1+2lim
q→0
8πe2
E c k?E v k?ω?i0+
.
(8)
In calculatingεM from Eq.(7),three valence bands,one conduction band and2048Monkhorst-Pack42special k points in the full Brillouin zone were used.An arti?cial broad-ening of0.05eV was introduced in spectral lines.Several
groups34,43,44have used low symmetry,shifted k points to achieve well converged excitonic spectra.Excitons in RGS belong to an intermediate regime,where they are localised in real space and delocalised in reciprocal space(see Section III). Convergence of excitonic spectra can therefore be achieved using special points only.65G vectors were used to calculate the direct part of the interaction,Eq.(4),and up to500were used for the exchange interaction,Eq.(5).An all-electron basis containing5s,4p and2d Cartesian Gaussian orbitals on the atomic nuclear site was used for Ne and a similar basis with7s,6p and4d orbitals on the atomic nuclear site plus2s, 2p and1d orbital on the octahedral interstitial site was used for Ar.The basis used for Ne is smaller than that used pre-viously for a GW calculation on Ne while the Ar basis is the same as used previously(basis set2in Ref.[35]).
III.RESULTS
A.Optical Spectra
1.Neon
The BSE eigenvalue problem was solved for Ne using an exciton exchange term which either included or omitted the LT splitting term(Eq.(6)).Exciton energies and binding en-ergies,E B=E g?E n,are given in Table I and are compared to earlier calculations.In the work by Andreoni et al.13,n=1 and n′=1excitons were calculated using matrix elements and a band structure from an augmented plane wave(APW) calculation and excitons with higher principal quantum num-bers were calculated using the effective mass approximation (EMA).In the work by Martinelli and Pastori Parravicini45 the electron-hole attraction term in the integral equation was treated using a model screened Coulomb potential.Experi-mental exciton energies in Table I are from optical transmis-sion data by Saile and Koch4.Both L and T excitons were observed in thin?lm optical absorption data and the L exci-ton energy of17.75eV from the BSE calculation is in good agreement with a value of17.74eV from electron energy loss data10.
The imaginary part of the macroscopic dielectric function,ε2,derived from Kramers-Kronig transformation of re?ec-
2
4
6
8
10
16182022
16182022
ε
2
ω [eV]
GAP
Ne
x10
x10
BSE
EXP
FIG.1:Imaginary part of the macroscopic dielectric function for Ne calculated using BSE wave functions and from experimental data by Skibowski19.
TABLE I:Exciton energy levels,E n,band gaps,E g,binding en-ergies,E B and LT splittings in solid Ne in eV.Theoretical results from an augmented plane wave(APW)calculation for the n=1 and n′=1states and an effective mass approximation(EMA)cal-culation for n and n′>1,a model screened electron-hole poten-tial calculation and a BSE calculation are compared to experimental peak positions in optical transmission data.The APW and EMA calculations include spin-orbit coupling.Fundamental band gaps and longitudinal-transverse splittings,?LT,are given in the last two rows.
n E n a E n b E n c E B c E n d E B d
E g21.6721.6921.6921.58
?LT e0.230.300.25
a APW/EMA calculation Ref.13.
b SK calculation Ref.45.
c BSE calculation This work.
d Experiment Ref.4.
e j=1/2exciton.
tion measurements by Skibowski19and a BSE calculation(Eq.
(7))for singlet states without the LT splitting in the exchange term are shown in Fig.1.The experimental spectrum shows excitonic absorption at17.49,20.24,20.87and21.30eV19. These are the n′=1,2,3,4(singlet)exciton energies for Ne and they are nearly all coincident with data for Ne by Saile
4
and Koch4(Table I),where data for triplet exciton energies are available also.Singlet and triplet BSE calculations show the?rst two exciton absorption features at17.45(17.25)and 19.95(19.90)eV.While there is good agreement between re-sults of the BSE calculation and experiment for n′and n=1 states,exciton binding energies for n′and n>1are overes-timated.This may be a result of incomplete screening of the electron-hole interaction caused by the limited basis set used in this calculation.Differences in n and n′binding energies decrease with increasing quantum number.Singlet/triplet en-ergy splittings in BSE calculations for the?rst two states are 0.20and0.05eV and these compare to0.14and0.11eV in experiment(Table I).For higher states the BSE predicts es-sentially no splitting while a small splitting is still found in experiment.
When the LT splitting term(Eq.6)is included in the singlet state exchange,the n′=1exciton shifts to17.75eV,which corresponds to an LT splitting of0.30eV.The experimental LT splitting energy in the n=1′exciton is0.25eV and the calculation by Andreoni et al.13gave a value of0.23eV.The L exciton energy coincides with the experimental value of17.75 eV determined by optical absorption in a thin?lm4and a value of17.74eV obtained from electron energy loss experiments10. The LT splitting for the n′=2exciton from a BSE calculation is much smaller and has a value of0.03eV.Energies of T excitons remain essentially the same when the exchange term in Eq.(6)is included.
2.Argon
Singlet and triplet exciton energies and binding energies for Ar derived from BSE calculations and experiment are given in Table II.Experimental exciton binding energies in Ar are reproduced well in parametrized calculations by Andreoni et al.12and by Baroni et al.17.Binding energies from BSE calcu-lations are also in good agreement with experiment,although BSE exciton energy levels lie below experimental values be-cause the band gap is underestimated by0.5eV in the GW calculation used to generate the quasiparticle energies in Eq.
3.Exciton binding constants for j=3/2and j=1/2states have been estimated from experiment6,46.By?tting n and n′>1exciton peak positions to a Wannier plot(i.e.with no quantum defect)we?nd B ex to range between2.06and2.23 eV for the j=1/2exciton and between2.17and2.30eV for the j=3/2exciton.These values are in good agreement with collected data by Bernstorff et al.2
4.When the n and n′=2 levels from the BSE calculation are?tted we?nd a binding constant of2.56eV and when we use the n and n′=3lev-els we?nd a binding constant of2.16eV.The experimental LT splitting energy in the n=1′exciton is0.15eV.The LT splittings derived from the BSE calculation(0.36eV)is signi?cantly larger than that derived from the calculation by Andreoni et al.12(0.19eV)and the experimental value.
The imaginary part of the macroscopic dielectric function from experiment and a BSE calculation for the j=1/2exci-ton are shown in Fig.2.The experimental optical spectrum contains both the n=1and n′=1peaks because spin-TABLE II:Exciton energy levels,E n,band gaps,E g,binding en-ergies,E B,LT splittings and binding constants,B ex,in solid Ar in eV.Theoretical results from an augmented plane wave(APW)cal-culation for the n=1and n′=1states and an effective mass ap-proximation(EMA)calculation for n and n′>1,a model screened electron-hole potential calculation and a BSE calculation are com-pared to experimental peak positions in optical transmission data. The APW and EMA calculations include spin-orbit coupling.Funda-mental band gaps,longitudinal-transverse splittings,?LT,and bind-ing constants from are given in the last three rows.
n E B a E B b E n c E B c E n d E B d E g13.6914.25
?LT e0.190.360.15
B ex2.562.06
a Ref.12.
b Ref.17.
c BSE calculation This work.
d Experiment Ref.6.
e j=1/2exciton.
TABLE III:Fitted exciton binding constants,B ex,and band gaps, E g,in solid Ar in eV.n and n′>1levels have been used for raw experimental data.The n=2and n′=2energies and the GW value for E g have been used for BSE data and result in the same binding energies for j=1/2and j=3/2series.
j B ex a E g a B ex b E g b B ex c E g c
5
024681012141618202224101214161820
10121416
18
ε2
ω [eV] Exp
ω [eV] Theory G A P
Ar
x5
x5
BSE
EXP
FIG.2:Imaginary part of the macroscopic dielectric function for Ar calculated using BSE wave functions and from experimental data by Saile 19.The fundamental gap predicted by the GWA calculation for Ar is less than the experimental gap by 0.5eV .The scale for the BSE spectrum has been shifted by 0.5eV in order to align fundamental gaps in theory and experiment and facilitate comparison of experi-mental and theoretical
spectra.
2
distance from the hole [a.u]
2 distance from the electron [a.u]
FIG.4:Same as
Fig.3along the line AB :electron distribution (left panel)and hole distribution (right panel).Blue circles present atom positions.
onto nearest neighbor sites.A more quantitative display of the electron-hole correlation function is obtained by plotting the modulus squared of the wave function along a line con-taining three Ar atoms (Fig.(4)).These results con?rm ear-lier conclusions 2,11,47that the ?rst exciton is delocalized over nearest neighbor atoms and give for the ?rst time detailed in-formation on the structure of correlated electron-hole func-tions in Ar in real space.
IV .CONCLUSIONS
An exciton Hamiltonian has been diagonalized to obtain singlet and triplet exciton series for Ne up to n =5and Ar up to n =3.Exciton binding energies for n ′=1singlet and n =1triplet excitons for both Ne and Ar are in excellent agreement with experiment.The longitudinal-transverse split-ting of the n ′=1singlet excitons in Ne is in good agreement with experiment;while the value obtained from a BSE cal-culation for Ar exceeds the experimental value (0.36eV c.f.0.15eV),one might expect Ar to have a larger splitting than Ne,as predicted by the BSE calculation (0.36eV c.f.0.30eV),because of a larger polarisability density in Ar.
The band gap for Ne derived from a GW calculation is 21.69eV and agrees very well with the experimental value of 21.58eV .The band gap for Ar from a GW calculation is 13.69eV and underestimates the experimental value of 14.25eV by 4%.The excellent agreement between theory and ex-periment for the band gap of Ne is fortuitous and is a result of using a relatively small basis set with functions located only on atomic sites.When s and p Gaussian orbitals were added to the basis at octahedral interstitial sites of the fcc lattice,the GW band gap was reduced to 20.04eV 35,an underes-timate of the experimental value by 7%.Underestimation of experimental band gaps to this extent is typical of perturbative GW calculations which start with self-consistent Kohn-Sham Hamiltonians,as this work does.
Overestimation of exciton binding energies with n ≥2for Ne,but not for Ar,for which a superior basis set was used,suggests that the limited basis set used for Ne does not ade-quately account for screening of the electron-hole attraction
6
for more extended excitons.When a BSE calculation was performed for Ne using a basis which contained additional interstitial site basis functions,the optical spectrum contained spurious features above the?rst exciton absorption,although the GW calculation with this basis set35did not suffer from similar problems.Binding energies of n=1and n′=1exci-tons are expected to be much less affected by underscreening than those with larger principal quantum numbers since the electron and hole are in close proximity in those states and Coulomb potential is poorly screened at that range.
Plots of correlated electron-hole wave functions for the n=1exciton in Ar show that the extent of delocalisation of the electron-hole pair is quite limited,con?rming that these excitons belong to an intermediate regime between Frenkel and Wannier types.
Acknowledgments
This work was supported by Enterprise-Ireland under Grant number SC/99/267and by the Irish Higher Education Author-ity under the PRTLI-IITAC2program.The authors wish to thank N.Vast for useful discussions.
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How to manage time Time treats everyone fairly that we all have 24 hours per day. Some of us are capable to make good use of time while some find it hard to do so. Knowing how to manage them is essential in our life. Take myself as an example. When I was still a senior high student, I was fully occupied with my studies. Therefore, I hardly had spare time to have fun or develop my hobbies. But things were changed after I entered university. I got more free time than ever before. But ironically, I found it difficult to adjust this kind of brand-new school life and there was no such thing called time management on my mind. It was not until the second year that I realized I had wasted my whole year doing nothing. I could have taken up a Spanish course. I could have read ten books about the stories of successful people. I could have applied for a part-time job to earn some working experiences. B ut I didn’t spend my time on any of them. I felt guilty whenever I looked back to the moments that I just sat around doing nothing. It’s said that better late than never. At least I had the consciousness that I should stop wasting my time. Making up my mind is the first step for me to learn to manage my time. Next, I wrote a timetable, setting some targets that I had to finish each day. For instance, on Monday, I must read two pieces of news and review all the lessons that I have learnt on that day. By the way, the daily plan that I made was flexible. If there’s something unexpected that I had to finish first, I would reduce the time for resting or delay my target to the next day. Also, I would try to achieve those targets ahead of time that I planed so that I could reserve some more time to relax or do something out of my plan. At the beginning, it’s kind of difficult to s tick to the plan. But as time went by, having a plan for time in advance became a part of my life. At the same time, I gradually became a well-organized person. Now I’ve grasped the time management skill and I’m able to use my time efficiently.
英语演讲稿：未来的工作 这篇《英语演讲稿范文：未来的工作》，是特地，希望对大家有所帮助！ 热门演讲推荐：竞聘演讲稿 | 国旗下演讲稿 | 英语演讲稿 | 师德师风演讲稿 | 年会主持词 | 领导致辞 everybody good afternoon:. first of all thank the teacher gave me a story in my own future ideal job. everyone has a dream job. my dream is to bee a boss, own a pany. in order to achieve my dreams, i need to find a good job, to accumulate some experience and wealth, it is the necessary things of course, in the school good achievement and rich knowledge is also very important. good achievement and rich experience can let me work to make the right choice, have more opportunities and achievements. at the same time, munication is very important, because it determines whether my pany has a good future development. so i need to exercise their municative ability. i need to use all of the free time to learn
数学快速计算法 二位数乘法速算总汇 1、两位数的十位相同的,而个位的两数则是相补的(相加等于10)女口:78 X 72= 37 X 33= 56 X 54= 43 X 47 = 28 X 22 46 X 44 (1) 分别取两个数的第一位,而后一个的要加上一以后,相乘。 (2) 两个数的尾数相乘,(不满十,十位添作0) 78X 72=5616 37 X 33=1221 56 X 54= 3024 43 X 47= 2021 (7+1) X 7=56 (3+1) X 3=12 (5+1) X 5=30 (4+1) X 4=20 8X 2=16 7 X 3=21 6 X 4=24 3 X 7=21 口决:头加1,头乘头,尾乘尾 2、两个数的个位相同,十位的两数则是相补的 如:36 X 76= 43 X 63= 53 X 53= 28 X 88= 79 X 39 (1) 将两个数的首位相乘再加上未位数 (2) 两个数的尾数相乘(不满十,十位添作0) 36X 76=2736 43 X 63=2709 3X 7+6=27 4 X 6+3=27 6X 6=36 3 X 3=9 口决:头乘头加尾,尾乘尾 3、两位数的十位差1,个位的两数则是相补的。 如:48 X 52 12 X 28 39 X 11 48 X 32 96 X 84 75 X 65
即用较大的因数的十位数的平方,减去它的个位数的平方。
48 X 52=2496 12 X 28 = 336 39 X 11= 819 48 X 32=1536 2500-4=2496 400-64=336 900-81=819 1600-64=1536 口决:大数头平方 —尾平方 4、一个乘数十位加个位是 9,另一个乘数十位和个位是顺数 X 78 = 81 X 23 = 27 X 89 = 5 23 2 如:12 X 13= 13 X 15= 14 X 15= 16 X 18= 17 X 19= 19 X 18= (1) 尾数相乘 ,写在个位上 (满十进位 ) (2) 被乘数加上乘数的尾数 12X 13=156 13 X 15= 195 14 X 15=210 16 X 18= 288 2X 3=6 3 X 5=154X 5=20 6 X 8=48 12+3=15 13+5=18 14+5=19 16+8=24 口决:尾数相乘 ,被乘数加上乘数的尾数 （满十进位 ） 6、任何二位数数乘于 11 如 :36 X 45 = 72 X 67 = 45 1 、解 : 3+1=4 4 X 4 = 1的6补5 数是 4X 5=20所以 36 X 45= 1620 2、解: 7+1=8 8 X 6 = 4的8补7 数是 8X 3=24所以 72 X 67 = 4824 3、解: 4+1=5 5 X 7=3的5补8 数是 5X 2=10所以 45 X 78 = 3510 5、10-20 的两位数乘法
关于坚持的英语演讲稿 Results are not important, but they can persist for many years as a commemoration of. Many years ago, as a result of habits and overeating formed one of obesity, as well as indicators of overall physical disorders, so that affects my work and life. In friends to encourage and supervise, the participated in the team Now considered to have been more than three years, neither the fine rain, regardless of winter heat, a day out with 5:00 time. The beginning, have been discouraged, suffering, and disappointment, but in the end of the urging of friends, to re-get up, stand on the playground. 成绩并不重要，但可以作为坚持多年晨跑的一个纪念。多年前，由于庸懒习惯和暴饮暴食，形成了一身的肥胖，以及体检指标的全盘失常，以致于影响到了我的工作和生活。在好友的鼓励和督促下，参加了晨跑队伍。现在算来，已经三年多了，无论天晴下雨，不管寒冬酷暑，每天五点准时起来出门晨跑。开始时，也曾气馁过、痛苦过、失望过，但最后都在好友们的催促下，重新爬起来，站到了操场上。 In fact, I did not build big, nor strong muscles, not a sport-born people. Over the past few years to adhere to it, because I have a team behind, the strength of a strongteam here, very grateful to our team, for a long time, we encourage each other, and with sweat, enjoying common health happy. For example, Friends of the several run in order to maintain order and unable to attend the 10，000 meters race, and they are always concerned about the brothers and promptly inform the place and time, gives us confidence and courage. At the same time, also came on their own inner desire and pursuit for a good health, who wrote many of their own log in order to refuel for their own, and inspiring. 其实我没有高大身材，也没健壮肌肉，天生不属于运动型的人。几年来能够坚持下来，因为我的背后有一个团队，有着强大团队的力量，在这里，非常感谢我们的晨跑队，长期以来，我们相互鼓励着，一起流汗，共同享受着健康带来的快
1.How to build a business that lasts100years 0:11Imagine that you are a product designer.And you've designed a product,a new type of product,called the human immune system.You're pitching this product to a skeptical,strictly no-nonsense manager.Let's call him Bob.I think we all know at least one Bob,right?How would that go? 0:34Bob,I've got this incredible idea for a completely new type of personal health product.It's called the human immune system.I can see from your face that you're having some problems with this.Don't worry.I know it's very complicated.I don't want to take you through the gory details,I just want to tell you about some of the amazing features of this product.First of all,it cleverly uses redundancy by having millions of copies of each component--leukocytes,white blood cells--before they're actually needed,to create a massive buffer against the unexpected.And it cleverly leverages diversity by having not just leukocytes but B cells,T cells,natural killer cells,antibodies.The components don't really matter.The point is that together,this diversity of different approaches can cope with more or less anything that evolution has been able to throw up.And the design is completely modular.You have the surface barrier of the human skin,you have the very rapidly reacting innate immune system and then you have the highly targeted adaptive immune system.The point is,that if one system fails,another can take over,creating a virtually foolproof system. 1:54I can see I'm losing you,Bob,but stay with me,because here is the really killer feature.The product is completely adaptive.It's able to actually develop targeted antibodies to threats that it's never even met before.It actually also does this with incredible prudence,detecting and reacting to every tiny threat,and furthermore, remembering every previous threat,in case they are ever encountered again.What I'm pitching you today is actually not a stand-alone product.The product is embedded in the larger system of the human body,and it works in complete harmony with that system,to create this unprecedented level of biological protection.So Bob,just tell me honestly,what do you think of my product? 2:47And Bob may say something like,I sincerely appreciate the effort and passion that have gone into your presentation,blah blah blah-- 2:56(Laughter) 2:58But honestly,it's total nonsense.You seem to be saying that the key selling points of your product are that it is inefficient and complex.Didn't they teach you 80-20?And furthermore,you're saying that this product is siloed.It overreacts, makes things up as it goes along and is actually designed for somebody else's benefit. I'm sorry to break it to you,but I don't think this one is a winner.
关于工作的优秀英语演讲稿 Different people have various ambitions. Some want to be engineers or doctors in the future. Some want to be scientists or businessmen. Still some wish to be teachers or lawers when they grow up in the days to come. Unlike other people, I prefer to be a farmer. However, it is not easy to be a farmer for Iwill be looked upon by others. Anyway,what I am trying to do is to make great contributions to agriculture. It is well known that farming is the basic of the country. Above all, farming is not only a challenge but also a good opportunity for the young. We can also make a big profit by growing vegetables and food in a scientific way. Besides we can apply what we have learned in school to farming. Thus our countryside will become more and more properous. I believe that any man with knowledge can do whatever they can so long as this job can meet his or her interest. All the working position can provide him with a good chance to become a talent. 1 ————来源网络整理，仅供供参考
一.两个20以内数的乘法 两个20以内数相乘,将一数的个位数与另一个数相加乘以10,然后再加两个尾数的积,就是应求的得数。如12×13＝156,计算程序是将12的尾数2,加至13里,13加2等于15,15×10＝150,然后加各个尾数的积得156,就是应求的积数。 二.首同尾互补的乘法 两个十位数相乘,首尾数相同,而尾十互补,其计算方法是:头加1,然后头乘为前积,尾乘尾为后积,两积连接起来,就是应求的得数。如26×24＝624。计算程序是:被乘数26的头加1等于3,然后头乘头,就是3×2＝6,尾乘尾6×4＝24,相连为624。 三.乘数加倍,加半或减半的乘法 在首同尾互补的计算上,可以引深一步就是乘数可加倍,加半倍,也可减半计算,但是:加倍、加半或减半都不能有进位数或出现小数,如48×42是规定的算法,然而,可以将乘数42加倍位84,也可以减半位21,也可加半倍位63,都可以按规定方法计算。48×21＝1008,48×63＝3024，48×84=4032。有进位数的不能算。如87×83＝7221,将83加倍166,或减半41.5,这都不能按规定的方法计算。 四.首尾互补与首尾相同的乘法 一个数首尾互补,而另一个数首尾相同,其计算方法是:头加1,然后头乘头为前积,尾乘尾为后积,两积相连为乘积。如37×33＝1221,计算程序是(3＋1)×3×100＋7×3＝1221。 五.两个头互补尾相同的乘法
两个十位数互补,两个尾数相同,其计算方法是:头乘头后加尾数为前积,尾自乘为后积。如48×68＝3264。计算程序是4×6＝24 24＋8＝32 32为前积,8×8＝64为后积,两积相连就得3264。 六.首同尾非互补的乘法 两个十位数相乘,首位数相同,而两个尾数非互补,计算方法:头加1,头乘头,尾乘尾,把两个积连接起来。再看尾和尾的和比10大几还是小几,大几就加几个首位数,小几就减掉几个首位数。加减的位置是:一位在十位加减,两位在百位加减。如36×35＝1260,计算时(3＋1)×3＝12 6×5＝30 相连为1230 6＋5＝11,比10大1,就加一个首位3,一位在十位加，1230＋30＝1260 36×35就得1260。再如36×32＝1152,程序是(3＋1)×3＝12,6×2＝12,12与12相连为1212,6＋2＝8,比10小2减两个3,3×2＝6,一位在十位减,1212－60就得1152。 七.一数相同一数非互补的乘法 两位数相乘,一数的和非互补,另一数相同,方法是:头加1,头乘头,尾乘尾,将两积连接起来后,再看被乘数横加之和比10大几就加几个乘数首。比10小几就减几个乘数首,加减位置:一位数十位加减,两位数百位加减,如65×77＝5005,计算程序是(6＋1)×7＝49，5×7＝35,相连为4935,6＋5＝11,比10大1,加一个7,一位数十位加。4935＋70＝5005 八.两头非互补两尾相同的乘法 两个头非互补,两个尾相同,其计算方法是:头乘头加尾数,尾自乘。两积连接起来后,再看两个头的和比10大几或小几,比10大几就加几个尾数,小几就减几个尾数,加减位置:一位数十位加减,两位数百位加减。如67×87＝5829,计算程序是:6×8＋7＝55,7×7＝49,相连为5549,6＋8＝14,比10大4,就加四个7,4×7＝28,两位数百位加,5549＋280＝5829
5.4.1 梁的剪力、弯矩方程和剪力、弯矩图 梁在外力作用下，各个截面上的剪力和弯矩一般是不相等的。若以横坐标表示横截面沿梁轴线的位置，则剪力Q 和弯矩M 可以表示为坐标的函数，即 它们分别称为梁的剪力方程和弯矩方程。 与绘制轴力图或扭矩图一样，可用图线表明梁的各截面上剪力和弯矩沿梁轴线的变化情况。作图时，取平行于梁轴线的直线为横坐标轴，值表示各截面的位置；以纵坐标表示相应截面上的剪力、弯矩的大小及其正负，这种表示梁在各截面上剪力和弯矩的图形，称为剪力图和弯矩图。 例5-1 简支梁AB 承受承受均布荷载作用，如图 5 - 10a 所示。试列出剪力方程和弯矩方程，并绘制剪力图和弯矩图。 解：(1) 计算支反力以整梁为研究对象，利用平衡条件计算支反力。由于简支梁上的载荷对于跨度中央截面是对称的，所以 A 、 B 两端的支反力应相等，即 (1) 方向如图。 (2) 建立剪力、弯矩方程以梁左端A 为的坐标原点，取坐标为的任意横截面的左侧梁段为研究对象。设截面上的剪力Q () 、弯矩M () 皆为正，如图5-10b 所示。由平衡方程
将(1) 式代入上面两式，解得 （ 2 ） （ 3 ） (2) 、(3) 两式分别为剪力方程和弯矩方程。 (3) 绘制剪力图、弯矩图由式(2) 可知，剪力图为一直线。只需算出任意两个截面的剪力值，如A 、B 两截面的剪力，即可作出剪力图，如图5 - 10c 所示。 由式(3) 可知，弯矩图为一抛物线，需要算出多个截面的弯矩值，才能作出曲线。例如计算下列五个截面的弯矩值：当时, M =0 ；当 时，；当时，。由此作出的弯矩图，如图5-10d 所示。 由剪力图和弯矩图可知，在靠近A 、B 支座的横截面上剪力的绝对值最大，其值为 在梁的中央截面上，剪力Q ＝0 ，弯矩为最大，其值为 例5-2 简支梁AB 承受集中力偶M0作用，如图 5 - 11a 所示。试作梁的剪力图、弯矩图。
尊敬的领导，老师，亲爱的同学们， 大家好！我是5班的梁浩东。今天早上我坐车来学校的路上，我仔细观察了路上形形色色的人，有开着小车衣着精致的叔叔阿姨，有市场带着倦容的卖各种早点的阿姨，还有偶尔穿梭于人群中衣衫褴褛的乞丐。于是我问自己，十几年后我会成为怎样的自己，想成为社会成功人士还是碌碌无为的人呢，答案肯定是前者。那么十几年后我怎样才能如愿以偿呢，成为一个受人尊重，有价值的人呢？正如我今天演讲的题目是：自主管理。 大家都知道爱玩是我们孩子的天性，学习也是我们的责任和义务。要怎样处理好这些矛盾，提高自主管理呢？ 首先，我们要有小主人翁思想，自己做自己的主人，要认识到我们学习，生活这一切都是我们自己走自己的人生路，并不是为了报答父母，更不是为了敷衍老师。 我认为自主管理又可以理解为自我管理，在学习和生活中无处不在，比如通过老师，小组长来管理约束行为和同学们对自身行为的管理都属于自我管理。比如我们到一个旅游景点，看到一块大石头，有的同学特别兴奋，会想在上面刻上：某某某到此一游话。这时你就需要自我管理，你需要提醒自己，这样做会破坏景点，而且是一种素质低下的表现。你设想一下，如果别人家小孩去你家墙上乱涂乱画，你是何种感受。同样我们把自主管理放到学习上，在我们想偷懒，想逃避，想放弃的时候，我们可以通过自主管理来避免这些，通过他人或者自己的力量来完成。例如我会制定作息时间计划表，里面包括学习，运动，玩耍等内容的完成时间。那些学校学习尖子，他们学习好是智商高于我们吗，其实不然，在我所了解的哪些优秀的学霸传授经验里，就提到要能够自我管理，规范好学习时间的分分秒秒，只有辛勤的付出，才能取得优异成绩。 在现实生活中，无数成功人士告诉我们自主管理的重要性。十几年后我想成为一位优秀的，为国家多做贡献的人。亲爱的同学们，你们们？让我们从现在开始重视和执行自主管理，十几年后成为那个你想成为的人。 谢谢大家！
关于工作的英语演讲稿 【篇一：关于工作的英语演讲稿】 关于工作的英语演讲稿 different people have various ambitions. some want to be engineers or doctors in the future. some want to be scientists or businessmen. still some wish to be teachers or lawers when they grow up in the days to come. unlike other people, i prefer to be a farmer. however, it is not easy to be a farmer for iwill be looked upon by others. anyway,what i am trying to do is to make great contributions to agriculture. it is well known that farming is the basic of the country. above all, farming is not only a challenge but also a good opportunity for the young. we can also make a big profit by growing vegetables and food in a scientific way. besides we can apply what we have learned in school to farming. thus our countryside will become more and more properous. i believe that any man with knowledge can do whatever they can so long as this job can meet his or her interest. all the working position can provide him with a good chance to become a talent. 【篇二：关于责任感的英语演讲稿】 im grateful that ive been given this opportunity to stand here as a spokesman. facing all of you on the stage, i have the exciting feeling of participating in this speech competition. the topic today is what we cannot afford to lose. if you ask me this question, i must tell you that i think the answer is a word---- responsibility. in my elementary years, there was a little girl in the class who worked very hard, however she could never do satisfactorily in her lessons. the teacher asked me to help her, and it was obvious that she expected a lot from me. but as a young boy, i was so restless and thoughtless, i always tried to get more time to play and enjoy myself. so she was always slighted over by me. one day before the final exam, she came up to me and said, could you please explain this to me? i can not understand it. i
简单载荷 梁内力图（剪力图与弯矩图） 梁的简图 剪力Fs 图 弯矩M 图 1 l a F s F F l a F l a l -+ - F l a l a ) (-+ M 2 l e M s F l M e + M e M + 3 l a e M s F l M e + M e M l a l -e M l a + - 4 l q s F + -2 ql 2 ql M 8 2ql + 2 l 5 l q a s F + -l a l qa 2) 2(-l qa 22 M 2 228)2(l a l qa -+ l a l qa 2) (2 -l a l a 2)2(- 6 l q s F + -3 0l q 6 0l q M 3 92 0l q + 3 )33(l - 7 a F l s F F + Fa -M
8 a l e M s F + e M M 9 l q s F ql + M 2 2ql - 10 l q s F 2 l q + M 6 20l q - 注：外伸梁 = 悬臂梁 + 端部作用集中力偶的简支梁 表2 各种载荷下剪力图与弯矩图的特征 某一段梁上的外力情况 剪力图的特征 弯矩图的特征 无载荷 水平直线 斜直线 或 集中力 F 突变 F 转折 或 或 集中力偶 e M 无变化 突变 e M 均布载荷 q 斜直线 抛物线 或 零点 极值 表3 各种约束类型对应的边界条件 约束类型 位移边界条件 力边界条件 （约束端无集中载荷） 固定端 0=w ,0=θ — 简支端 0=w 0=M
Dear teacher and colleagues: my topic is on “spare time”. It is a huge blessing that we can work 996. Jack Ma said at an Ali's internal communication activity, That means we should work at 9am to 9pm, 6 days a week .I question the entire premise of this piece. but I'm always interested in hearing what successful and especially rich people come up with time .So I finally found out Jack Ma also had said :”i f you don’t put out more time and energy than others ,how can you achieve the success you want? If you do not do 996 when you are young ,when will you ?”I quite agree with the idea that young people should fight for success .But there are a lot of survival activities to do in a day ,I want to focus on how much time they take from us and what can we do with the rest of the time. As all we known ,There are 168 hours in a week .We sleep roughly seven-and-a-half and eight hours a day .so around 56 hours a week . maybe it is slightly different for someone . We do our personal things like eating and bathing and maybe looking after kids -about three hours a day .so around 21 hours a week .And if you are working a full time job ,so 40 hours a week , Oh! Maybe it is impossible for us at
关于人英语演讲稿(精选多篇) 关于人的优美句子 1、“黑皮小子”是我对在公交车上偶遇两次的一个男孩的称呼代号。一听这个外号，你也定会知道他极黑了。他的脸总是黑黑的；裸露在短袖外的胳膊也是黑黑的；就连两只有厚厚耳垂的耳朵也那么黑黑的，时不时像黑色的猎犬竖起来倾听着什么；黑黑的扁鼻子时不时地深呼吸着，像是在警觉地嗅着什么异样的味道。 2、我不知道，如何诠释我的母亲，因为母亲淡淡的生活中却常常跳动着不一样的间最无私、最伟大、最崇高的爱，莫过于母爱。无私，因为她的爱只有付出，无需回报；伟大，因为她的爱寓于
普通、平凡和简单之中；崇高，是因为她的爱是用生命化作乳汁，哺育着我，使我的生命得以延续，得以蓬勃，得以灿烂。 3、我的左撇子伙伴是用左手写字的，就像我们的右手一样挥洒自如。在日常生活中，曾见过用左手拿筷子的，也有像超级林丹用左手打羽毛球的，但很少碰见用左手写字的。中国汉字笔画笔顺是左起右收，适合用右手写字。但我的左撇子伙伴写字是右起左收的，像鸡爪一样迈出田字格，左看右看，上看下看，每一个字都很难看。平时考试时间终了，他总是做不完试卷。于是老师就跟家长商量，决定让他左改右写。经过老师引导，家长配合，他自己刻苦练字，考试能够提前完成了。现在他的字像他本人一样阳光、帅气。 4、老师，他们是辛勤的园丁，帮助着那些幼苗茁壮成长。他们不怕辛苦地给我们改厚厚一叠的作业，给我们上课。一步一步一点一点地给我们知识。虽然
他们有时也会批评一些人，但是他们的批评是对我们有帮助的，我们也要理解他们。那些学习差的同学，老师会逐一地耐心教导，使他们的学习突飞猛进。使他们的耐心教导培养出了一批批优秀的人才。他们不怕辛苦、不怕劳累地教育着我们这些幼苗，难道不是美吗？ 5、我有一个表妹，还不到十岁，她那圆圆的小脸蛋儿，粉白中透着粉红，她的头发很浓密，而且好像马鬓毛一样的粗硬，但还是保留着孩子一样的蓬乱的美，卷曲的环绕着她那小小的耳朵。说起她，她可是一个古灵精怪的小女孩。 6、黑皮小子是一个善良的人，他要跟所有见过的人成为最好的朋友！这样人人都是他的好朋友，那么人人都是好友一样坦诚、关爱相交，这样人与人自然会和谐起来，少了许多争执了。 7、有人说，老师是土壤，把知识化作养分，传授给祖国的花朵，让他们茁壮成长。亦有人说，老师是一座知识的桥梁，把我们带进奇妙的科学世界，让
关于时间的英语演讲稿范文_演讲稿 and organizing people to learn from advanced areas to broaden their horizons in order to understand the team of cadres working conditions in schools, the ministry of education has traveled a number of primary and secondary schools to conduct research, listen to the views of the school party and government leaders to make school leadership cadres receive attention and guidance of the ministry of education to carry out a variety of practical activities to actively lead the majority of young teachers work hard to become qualified personnel and for them to put up the cast talent stage, a single sail swaying, after numerous twists and turns arrived in port, if there is wind, a hand, and naturally smooth arrival and guide students to strive to e xcel, need to nazhen “wind” - teacher. teachers should be ideological and moral education, culture education and the needs of students organically combining various activities for the students or students to carry out their own. for example: school quiz competitions, essay contests, ke benju performances and other activities to enable students to give full play to their talents. teachers rush toil, in order to that will enable students to continue to draw nutrients, to help them grow up healthily and become pillars of the country before. for all students in general education, the government departments have also not forget those who cared about the