文档介绍：该【固体物理作业题 】是由【1781111****】上传分享，文档一共【12】页，该文档可以免费在线阅读，需要了解更多关于【固体物理作业题 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。:..::(a)Showthatthepackingfractionfforthediamondlatticeis3/16.(b)blattice?:Considerthehexagonalclosepackedlattice.(a)Showthat=a83=.(b)Showthatthepackingfractionfortheidealhcplatticeisπ2/6=:poundA+B-=r/<1.+::Usetheinformationinthetextbooktocalculatethedensities(inkgm-3)ofthefollowingsolids:(a)Aluminum,(b)Iron,(c)Siliconand(d):..,upythecubefaces.(a)WhatistheBravaislatticetype?2(b)VerifythattheprimitiveunitcellcontainsoneSr,oneTiandthreeOatoms.(c):TheprimitivelatticevectorsofacertainBravaislatticecanbewrittenRnnaxnbynz21213(2)12=1+++Whatisthelatticetype?:,.(a)Basecenteredcubic(simplecubicwithadditionalpointsinthecentersofthehorizontalfacesoftheell).(b)Sidecenteredcubic(simplecubicwithadditionalpointsinthecentersoftheverticalfacesofthecubiccell).(c)Edgecenteredcubic(simplecubicwithadditionalpointsatthemidpointsofthelinesjoiningnearestneighbors).:指出体心立方晶格(111)面与(100)面,(111)面与(110)的交线的晶向。作业题2:..:(i)Whatisalattice?Expressalatticemathematically.(iii)binealatticewithabasistoobtainacrystalstructure?:(i)Whatarethe3fundamentaltranslationvectors?(ii)Showwith2dimensionalexamples,howthefundamentaltranslationvectorsmaydefineeitheranon-primitive(conventional)unitcelloraprimitiveunitcell.(iii)Expressmathematicallythesize(areain2dimensional&volumein3dim):(i)WhatisaBravaislattice?(ii)Drawthefive2-?:(i)Howmany3dimensionalBravaislatticesarepresent?(ii)Howmany3dimensionalcrystalsystemsarethere?(iii)MakeaTablehavingthefollowingcolumns:LatticeSystem--Bravaislattice--DiagramofConventionalunit--Name&Symbolunitcell--:(i)Whatdoyoumeanbypackingfraction?(ii)Calculatethepackingfractioninasimplecubic,basecenteredcubicandafacecenteredcubicstructures.(iii)Inwhichstructurearetheatomsmostcloselypacked?作业题3:..2(v)ExplainwithdiagramtheNaClstructureandtheCsClstructure?Whatisthestructureofdiamond?:(i)Whatarecrystalplanes?(ii)WhatdotheMillerIndicesrepresent?(iii)Whatdothefollowingindicesrepresent?(hkl),{hkl},[hkl]and<hkl>?(iv)Drawtheunitcell&thefollowingplanesinasimplecubiclattice:(100),(ī00),(200),(1ī1),(201),(2ī0),(122).(v)Whatdoyoumeanbycrystallatticeinterplanarspacing(dhkl)?(vi):(i)Whatisthedensityofatoms(numberperunitarea)ona(111)lattice?(ii)Whatisthedensityofatoms(numberperunitarea)ona(110)lattice?:(i)ConstructtheWigner-Seitzprimitivecellsforone-dimensionallattice.(ii)ConstructtheWigner-blattice(.,hexagonallattice)(2D).(iii)ConstructtheWigner-Seitzprimitivecellsforsimplecubic,body-centeredcubicandface-centeredcubiclattices(3D),:(i)Constructthereciprocallatticefortwo-dimensionalrectangularlattice,squarelattice,作业题4:..obliquelatticeandhexagonallattice.(ii)Constructthereciprocallatticesforsimplecubic,body-centeredcubicandface-:(i)ConstructthefirstBrillouinzonefortwo-dimensionalrectangularlattice,squarelattice,obliquelatticeandhexagonallattice.(ii)ConstructthefirstBrillouinzoneforsimplecubic,body-centeredcubicandface-:考虑晶格中的一个晶面hkl。(i)证明倒格矢垂123rvvv=++直于这个晶面。(ii)证明晶格中两个相邻平行晶面的间距为Ghkldr2()=(iii)证明对于简单立方晶格有d=a/h+k+:证明第一布里渊区的体积为(2π)3/Vc。其中Vc是晶格原胞的体积。提示:布里渊区的体积等于傅里叶空间中的初基平行六面体的体积,同时利用矢量恒等式(c×a)×(a×b)=(c?a×b):(i)ExplaininshorthowX--?(StatedeBroglieshypothesisofmatter作业题5:..:=h/p).θ=nλ).Visiblelightcannotbeusedtostudydiffractionbycrystals,why?(iii)TheBraggangleforreflectionfromthe(111)planesinAl(fcc)-raywavelengthofλ=:(i)thelengthofthecubeedgeoftheunitcell;(ii)theinterplanardistancefortheseplanes.().:4Anx-raysourceemitsanx-raylineofwavelengthl=.(i)FindtheBraggangle(s)forreflectionsfromthe(111)planesofAl.(ii)FindtheBraggangle(s)forreflectionsfromthe(110):Theprimitivelatticevectorsofa2-dimensionaltriangularlatticearerr=;baiajrrr232=+whereaisthenearestneighbordistance.(i)Findthereciprocallattice(ii)DrawtheWignerSeitzcellandlocatethecoordinatesofitscorners.(iii):AnX-?作业题6:..(a)GiveaqualitativeinterpretationontheoriginoftheVanderWaalsforce.(b)-Jonespotential???126()-4---JonesparametersforinertgasesElementσ(angstrom)ε(eV)(a)PlottheLennard-JonespotentialandforcefortheinertgasesNe,Ar,KeandXe,respectively.(b).(c)(parewiththeresultfoundinTable4(,).:..(a)CalculatetheCoulombenergybetweenaK+andaCl-ionatthenearestneighbourdistanceinunitsofeV.(b)AssumethattheparameterssandeofthevanderWaalsattractionbetweentheions(thetermproportionalto1/r6intheLennard-Jonespotential)arethesameasforAr().CalculatethevanderWaalsenergybetweenaK+andaCl-parewiththeresultfoundunder(a).-()(a)Findtheequilibriumspacingbetweentheatoms.(b)Findthesoundvelocity.(c)Whatisthemaximumfrequency?-1withthespacingconstantK1andtomassesn+2andn-’thmassisnow作业题8:..)()muKuu-2uKuu-2u=+++&&nnn11-122-2++AssumeperiodicboundaryconditionsandsolutionsoftheformuAe=i(kan-t)nwhereaisequilibriumlatticespacing.(a)Findaformulaforwasafunctionofk.(b)Plotωm/KvskaforthespecialcaseK=(a)TheFermienergy(b)TheFermivelocity(c)×10-×10-,10K,100KinunitsofJmol-1K-(angstrom)c(angstrom)(at4K):..(diamond)(4K)(4K)(4K)=×10-:..?:Thevolumeink-spacecorrespondingtooneallowedk-/L)3,-=2(U0/V)/=-V(dp/dV)ofanelectrongasatT=0isB=5p/3=10U0/-=0K,theconductionelectronsatthebottomofthebandhaveanenergyE=0andtheconductionelectronswiththehighestenergyhaveanenergyE=-dimensions,whatistheaverageenergyoftheconductionelectrons?-()lnexp1lnexp12kTkTEmkTTkTnhFμ,:..=,thespecificheat,theentropy,(k),D(E)m/(h).Whatistheheatcapacityforafreeelectrongasintwo2dimensions?,calculatethebandstructuresofasimplecubiclatticealongkxdirection<100>.,calculatethebandstructuresofasimplecubiclatticealongdirection<111>.,pleasedrawthebandstructuresforatwo-:V=,a=2×10-10m,b=5×10-,