中南大学版固体物理学习题及答案详解

1.2.3.BravaisBravaisBravais224.1.34abcd1.34a”bcda12126bc+1+6212d48485.aba1a2ababab6.KX1a2a3a2⎪⎪⎪⎭⎪⎪⎪⎬⎫Ω×=Ω×=Ω×=][2][2][2213132321aabaabaabπππΩ][321aaa×⋅=Ω7.Miller321hhhhklMillerbc321hhh1a2a3ahkla8.1001101111001101111001101111001101111001101119.1.35334262623410.71.1126886411.16π283π362π462π5163π1RRa2=6)2(3413413333πππα=⋅=⋅=RRaR2R3/4Ra=83)3/4(3423423333πππα=⋅=⋅=RRaR3RRa22=62)22(3423443333πππα=⋅=⋅=RRaR44RRa2=Rac)3/64()3/62(==62)3/64(4)2(363464363462323πππα=⋅⋅=⋅⋅=RRRcaR5RRa)3/8(=163)3/8(34834833333πππα=⋅=⋅=RRaR12.⎪⎪⎪⎩⎪⎪⎪⎨⎧−+=+−=++−=)(2)(2)(2321kjiakjiakjiaaaa⎪⎪⎪⎩⎪⎪⎪⎨⎧+=Ω×=+=Ω×=+=Ω×=)(2][2)(2][2)(2][2213132321jiaabkiaabkjaabaaaππππππ13.jiaaa2321+=jiaaa2322+−=kac=35][2321321aaaaab×⋅×=π)]()232[()232()()232(2kjijikjicaaaacaa×+−⋅+×+−=πcaacac2232232ji+=π)32(2ji+aπ][2321132aaaaab×⋅×=π)]()232[()232()232()(2kjijijikcaaaaaac×+−⋅++−×=πcaacac2232232ji+−=π)32(2ji+−aπ][2321213aaaaab×⋅×=π)]()232[()232()232()232(2kjijijijicaaaaaaaa×+−⋅++−×+=πcaa2223232kπ==kcπ214.ma10104−×=mb10106−×=mc10108−×=o90=αo90=βo120=γ123(210)(1)ai=1a)2321(2jia+−=bkac=36][2321321aaaaab×⋅×=π=abcbc23)2123(2ji+π=)31(2ji+aπ][2321132aaaaab×⋅×=π=abcac232jπ=j322⋅bπ][2321213aaaaab×⋅×=π=abcab23232kπ=k⋅cπ21b22)31(12+⋅aπ110108138.134−×=maπ2b2)32(2⋅bπ110102092.134−×=mbπ3b212⋅cπ110107854.02−×=mcπ(2)][321aaa×⋅=Ω)]()2321([)(kjiicba×+−⋅328106628.123mabc−×=][321bbb×⋅=Ω∗)](2)32(2[)31(2kjjicbaπππ×⋅+3303104918.1316−×=mabcπ(3)(210)hhdKπ2==3210122bbb++π=ji)3434(42baaππππ++=mbaa1022104412.1)3131()1(142−×=++⋅ππ15.1.361EDFDOF2,AGKFGIHMNLK73120131a2xyzABDCGFEOIHyxAa2KOGLNMz1.361ED[111][110]OF[011]FD21-11AGKxyz1:1:111:11:11=−1111/21FGIHxyz1:0:211:1:2/11=∞2011/2-1MNLKxyz0:1:21:11:2/11=∞−2103120131AMLkABC8b3xyzABCOyxAb2KOLMz16.abc)(hkl222)()()(1clbkahdhkl++=⎪⎩⎪⎨⎧===kajaiacba321⎪⎪⎪⎩⎪⎪⎪⎨⎧==×⋅×===×⋅×===×⋅×=kkaaaaabjjaaaaabiiaaaaabcababcbacabcabcabcπππππππππ2)(2][][22)(2][][22)(2][][232121332113232132132122bbbKlkhdhklhkl++==ππ222)()()(12222clbkahlckbha++=++=kjiππππ17.ia31=ja32=)(5.13kjia++=12312145[111][111]12⎪⎪⎪⎩⎪⎪⎪⎨⎧=⋅=×⋅×=−=−⋅=×⋅×=−=−⋅=×⋅×=kkaaaaabkjkjaaaaabkikiaaaaab5.125.1392][][2)(325.13)(5.42][][2)(325.13)(5.42][][2321213321132321321πππππππππ312193211121122122bbbK−+⋅==ππd103030352(322==−+=kjiππ4dρβ=dρρ)(321hhh321hhhd33221122321321bbbKhhhdhhhhhh++==ππmax)2(3])2([3222132121321=−−++=−−++=kjikjihhhhhhhhhhππ1000101010111112/35[111][111]321321321321111111111111)()(arccosaaaaaaaaaaaaRRRR−+⋅++−+⋅++=⋅⋅=αo53.485.15.15.15.15.45.4)5.15.15.1()5.15.45.4(arccos=−+⋅++−+⋅++=kjikjikjikji18.GaAsGaAsd2.4510-10m(1)(2)(3)(110)(4)(110)(111)(1)GaAsGaAsGaAsGa1/4ad43=GaAs10mda101045.23434−××===m101059.5−×(2)GaAs⎪⎪⎪⎩⎪⎪⎪⎨⎧+×=+=+×=+=+×=+=−−−)(10795.2)(2)(10795.2)(2)(10795.2)(2103102101jijiaikikakjkjaaaa⎪⎪⎪⎩⎪⎪⎪⎨⎧−+×=−+=+−×=+−=++−×=++−=−−)(10124.1)(2)(10124.1)(2)(10124.1)(2103102101kjikjibkjikjibkjikjibaaaπππ(3)(110)mad1032111011010795.2201122−×==⋅+⋅+⋅==bbbKππ(4)(110)(111)110K111Kα321321321321111110111110111011)111()011(arccosbbbbbbbbbbbbKKKK⋅+⋅−⋅⋅⋅+⋅+⋅⋅+⋅−⋅⋅⋅+⋅+⋅=⋅⋅=αo55.107)3015.0arccos(=−19.1.37a(1)(2)(1)i1a1.37⎪⎩⎪⎨⎧+==jiaia23221aaa11⎪⎪⎩⎪⎪⎨⎧=×⋅×⋅=−=×⋅×⋅=jkaaakbjikaakabaa34)(2)31(2)(221122121ππππ(2)2ijar3222π==b20.14000212102102102121)(22jjjjlwkvhunijjijjhklefefF++⋅∑∑==πλπRS[])()()(1lknilhnikhnieeef++++++=πππ[]{222)(cos)(cos)(cos1lknlhnkhnfFhkl++++++=πππ[]}2)(sin)(sin)(sinlknlhnkhn++++++πππkl0hn[]222)(cos)(cos)(cos1lknlhnkhnfFhkl++++++=πππ12nknhnlnhnknl02=hklF22000212121)(22jjjjlwkvhunijjijjhklefefF++⋅∑∑==πλπRS[])(1lkhnief+++=π[][]{}2222)(sin)(cos1lkhnlkhnfFhkl++++++=ππkl0hn[]222)(cos1lkhnfFhkl+++=π)(lkhn++02=hklF38000414141212102102102121414343434341434143)(22jjjjlwkvhunijjijjhklefefF++⋅∑∑==πλπRS⎥⎦⎤⎢⎣⎡+++++++=+++++++++++)33(2)33(2)33(2)()()()(21lkhnilkhnilkhnilknilhnikhnilkhnieeeeeeefπππππππ[])()()()(211lknilhnikhnilkhnieeeef++++++++⎥⎦⎤⎢⎣⎡+=ππππ[{+++⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎥⎦⎤⎢⎣⎡+++⎥⎦⎤⎢⎣⎡+++=)(cos1)(2sin)(2cos12222khnlkhnlkhnfFhklπππ][]}22)(sin)(sin)(sin)(cos)(coslknlhnkhnlknlhn++++++++++πππππl0hkn[]2222)(cos)(cos)(cos1)(2cos1lknlhnkhnlkhnfFhkl++++++⎥⎦⎤⎢⎣⎡+++=ππππnhnknlnknlnh13nhnk)nl12(4)(+=++mlkhnm02=hklF21.XNaCl5.9NaClNaαKCl2.8210-10m2.16g/cm31X21NaClmNaCl11110101064.51082.22−−×=××=a10102221111026.331064.5111−−×=×=++=adm91011110702.69.5sin1026.32sin2−−×=××==oθλdm2NaClAMaN=⋅ρ43236310310038.61016.2)1064.5(5.5844×=××××==−ρaMNNaClA141.123247r52OFN50kJ/mol2.N0EEENb−=NbENE0E3.2220)(rf22)(ru0r0)(=rf)(ru0)(rf)(ru4.25.0V0Unmrrruβα+−=)([])9/(00VmnU0022VVdVUdVdVdPVK⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎠⎞⎜⎝⎛−=1dVdUP−=1N)(2)(2nmrrNruNUβα+−==2Nr3rNNvVβ==3β2/2=β2112312)(31)(0rNrnrmNdrdUNrdVdUnmRββαβ⋅⎟⎠⎞⎜⎝⎛−==++40011222(231)(rrnmVrnrmNrNdrddVdrdVUd=++⎭⎬⎫⎩⎨⎧⎥⎦⎤⎢⎣⎡−⋅=βαβ⎥⎦⎤⎢⎣⎡+−+−⋅=nmnmrnrmrnrmNV0002022033291βαβα50)(0=rdVdUnmrnrm00βα=5⎥⎦⎤⎢⎣⎡+−⋅=⎥⎦⎤⎢⎣⎡+−⋅=nmnmVrnnrmmNVrnrmNVdVUd00200202222291291)(00βαβα)(92929102000200020UVmnrrNVmnrmnrnmNVnmmn−=⎥⎦⎤⎢⎣⎡+−⋅−=⎥⎦⎤⎢⎣⎡+−⋅=βααβ661[])9/(9000200VmnUUVmnVK=−⋅=6.2=m10=nm4eV10103−×αβKErrru−=+−=10020)(βα10102)(11030=−=rrdrrduβα2eVm124=kE100103−×=r03A=19105.4−×=αeV·m2eV·m96109.5−×=β1027.rBrA−9ABmr100108.2−×=JU19108−×=⎪⎪⎩⎪⎪⎨⎧=+−=−=−09)(201000900rBrAdrduUrBrArU0r⎪⎪⎩⎪⎪⎨⎧=×+×−×−=×−×−−−−−0)108.2()108.2(9108108.2)108.2(210101019109