固体物理(胡安)课后答案

固体物理(胡安)课后 答案 八年级地理上册填图题岩土工程勘察试题省略号的作用及举例应急救援安全知识车间5s试题及答案 第一章 晶的结及其结性体构称1.1石墨结中的原子排列成如结所示的六角结～结结结是结结结是结式格子。结什结碳网状构它作出结一结所结结的结点结和初基元胞。构两 解,石墨结中原子排成的六角结结是结式格子。因结如结网状构 点和点的格点在晶格结中所结的地位不同～不完构并AB 全等价～平移A?B,平移后晶格结不能完全结原所以是结构 式格子。 ,,,,1.2在正交直角坐结系中～若矢量R=li+lj+lk～l123,,, j～～结结位向量。Error: Reference source not found结整。结下列情数况属ik 于什结点结, , ;a,当l结全奇或全偶结～ i, ;b,当l之和结偶结。数i 解, ,,,,Rlalala=++l112233 Error: Reference source not found ,,,=++liljlk123 ()l,l,l=0,?1,?2... 123 l+l+l当结全奇或全偶结结面心立方结点结～构当Error: Reference sourcel123not found之和结偶结是面心立方结数构 l+l+l=1.3 在上结中若Error: Reference source not found奇位上有结子数离～123 ++=lllError: Reference source not found偶位上有正子～结结一子晶数离离123 体属构于什结结, 解,是子晶～于结化结结。离体属构 1.4 ;a,分结结明～面心立方;fcc,和心立方;体bcc,点结的结用初基元胞三基 矢结结角相等～结fcc结Error: Reference source not found～结bcc结Error: Reference source not found;b,在金结石结中～作任意原子其四最近结原子的结结。结明任意结之结结角构与个两条 11 o'o'arccos10927?=arccos10927?=θ均结 33 解:;1,结于面心立方 ,,,,,,aaajk=+aik=+ Error: Reference source not found ()()2122 ,,,aaij=+()32 ,,,2 aaaa===1322 ,,,,aa 112oCOSaa ===60 12()aa212 ,,,,aa 123oCOSaa ===60 23()aa223 ,,oCOSaa =60 ()13 ;2,结于心立方体 ,,,,,,,,,,,,aaaaijk=?++aijk=?+aijk=+? 123()()()222 ,,,3 aaaa===1232 ,,,,aa 112'oCOSaa ==?=1292712()aa312 ,,,,aa 1o'13COSaa ==?=12927(),,13aa313 ,,o'COSaa =12927 23() ;3,结于金结石晶胞 ,,,,,,,,33 aijkaijkη=++η=??()()1244 23a,,?,,2 ηη1124 ===?COSηη ()1229a3ηη1224 Error: Reference source not found 1.5 结明,在六角晶系中密勒指结;数h,k,l,的晶面族结距结 Error: Reference source not found 1?222，，2:,++4hhkkl,,d=+,,,,223ac::，， ,, aba== 结明: 元胞基矢的结体 ,, aai= ,,,oobaij=?+cos60cos30 Error: Reference source not found ,,13=?+aiaj22 ,, Error: Reference source not found cck= a00 a332?=?=aac0222 00c ,,,,×2[bc]23,ππ?倒格子基矢 ==(i+j)aa3? ,,,,?2π[c×a]4π3 ==jb?3a ,,,×ab,2π[]2π? ==kcc? 倒格矢, ,,,,***Ghakblc=++hkl 22ππd==hkl,2,,晶面结距 ***Ghklha+kb+lc 2??,,,,,,,,,???????222222??? hakblchakblchkabklbchlac++=+++ + + 222)))((( 222,,,222???42π42π2π a=b=c= 3a3ac Error: Reference source not found Error: Reference source not 2,,??,,,,22π ???? found Error: Reference source not foundab =bc =0ac =0 3a Error: Reference source not found Error: Reference source not found Error: Reference source not found 1?22222 42424242ππππ 222dhklhk=+++ hkl 3333aaaa 1?2222 4hkkll++=+ 223ac 1.6 结明,底心正交的倒点结仍结底心正交的。 结明,结结六角点结的第一布里是一六角正柱渊区个棱体 底心正交点结的结用晶胞如结, ,,u,,,abaxy=+ Error: Reference source not found 2aax=122,,ππππ245m==0,,,,θacz=33333 abcV= 初结晶胞结体: Error: Reference source not found c2 ,211π,,,, baaxy= =?2π 倒易点结的基矢,Error: Reference123 Vab c source not found ,,,,24ππybaa= = Error: Reference231Vcc ,,22ππ,,baaZ= =source not found Error: Reference source not found312Vcc 结结基矢定的面是正交底心点结确 1.7 结明,正点结是其本身的倒易点结的倒格子。 V 结明,倒易点结初结元胞的结体:是初基元胞的结 体c ,,, Vbbb?= Error: Reference source not found123()c ,2π,,baa= Error: Reference source not found 123Vc,,2π2π,,,,baa= baa= Error: Reference source not found Error:231312VVcc Reference source not found ,,,Vaaa?=而 ()c123 2,,,,,, 2πbbaaaa = 233112()() Vc Error: Reference2,,,,,,,, 2π = ? aaaaaaaa31213112()() {} Vc source not found ABCDABDCABCD = ? ()()()() 2,,, 2π,由于 = bbaaaa()×?=0() 123121 aaa311Vc 2,,,2π()Vaaa= 而 Error: Reference source not()? =bbac312231Vc foundError: Reference source not found Error: Reference source not found 2,,,,2π(),bbbab = 1231()1Vc 32,,,()π= aaa()1232 Vc 32()π=Vc 3,,,2π()或:bbb =123,,,() aaa()123 ,,,, ××,,bbbb3121结在结明, =2π2π=,,,,,,aa12()?×()?×bbbbbb123123 ,, ×,bb122π=,,,a3()?×bbb123 2,,2π(),Error: Reference source not found又bba =231Vc 令,, bb ()21,c=2π,,,1bbb?()123 2 2(),1π=2a,,, π1Vbbb? c()123 3,,,2π()又,Error: Reference source not found代入 bbb=?()123Vc 3 2π()V,,,ccaa== Error: Reference source not found同理 1113V2π() c ,, ()b×b,,31,,,=c2π=aError: Reference source not found 22()b?b×b123 ,, ()b×b,,12,,,=c2π=a Error: Reference source not found33()b?b×b123 1.8 二结平面点结作结结明点结不可能有七重旋结结结。从称 m''ABama==2cosθcos1θ= 解, 2 ππ3m==0,, θ22 ππππ245m==1,,,,θ3333 m2,,2==θππError: Reference source not found 1.9 结解结结什结, ;a,四角;四方,晶系中有底心四角和面心四角点结。没 ;b,立方晶系中有底心立方点结。没 ;c,六角晶中只有结结六角点结。 解,;a,因结四方晶系加底心～失去会4次结。 ;b,因结立方晶系加底心～失去将Error: Reference source not found3 次结。 ;c, 六角晶系加底心失去会6次结。 1.10 结明,在结化结型子晶中晶面族;离体h,k,l,的衍射强度结 2 ff+,当;h,k,l,结偶数结AB 2 Iff?,当;h,k,l,结奇数结Error: Reference source not found hklAB 0～其它情况 ff其中Error: Reference source not foundError: Reference source notAB found分结结正结子的散射因子。如何用此结果结明离KCL晶中体h,k,l均结奇的衍数射消失, +?结明,Nacl初基原胞中有Error: Reference source not found和Error:NaClReference source not found结结子。两离 ,111 r:0,0,0,,AB A、B分结代 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf Error: Reference source not found()i 222 和Error: Reference source not found。 因此何结因子, 几构 ?++2ihxhxhxπ()112233iiiFhhhfe,,=(),123i ?i2hhh++()π1232=+ffeAB ffhhh+++,结偶 AB123= ffhhh?++,结奇AB123 2射强度,Error: Reference source not found,结于Error:IFhhh ()123 hhh++ff=Reference source not found结奇的衍射面数Error: Reference123ABsource not found结消光。会 1.11 结结结金结石结晶的消光法结。构体 解,金结石结中～金结石结胞有构8原子～坐结结,个碳 111111111333331313133 0,0,0,,,0,,0,,0,,,,,,,,,,,,,,,,,() 222222444444444444444 ?++2inhxhxhxπ()112233jjj几构何结因子 Error: Reference source not foundFfe=,hklj Ffinhkinklinlk=+?++?++?+1expexpexpπππ ()()(){}hkl 1 +?++ finhklexp()π 2 in πexp2expexp1? ++?++?++hkinklilh ()()() ππ 2 nnπ Ffihklihklnhknkl=+?++?++++++1expsin1coscosπππ()()()(){} hkl 22 2 nnππ f22hkl=++++++IFIhklhkl1cossin?()() hklhklhkl 22 衍射强度不结零,;1,nh nk nl 都结基。数 1nhnknl++;2,nh nk nl 都结偶;包括零,数,且Error:()2 Reference source not found也结偶。数 如不结足以上件～结结些面的衍射消失～例如金结石不可能到条找 ;3～2～1,或;2～2～1,的一结衍射斑～也不可能有;4～4～2,结结的 二结衍射斑点。 1.12 结明,在倒易空结中～当Error: Reference source not found落于一倒格矢 Error: Reference source not found垂直平分面上结～结生布拉格反射。 ,,22 结明,波矢结足当Error:kkk+=h Reference source not found结有Error: ,,, khkk +=0Reference source not found h 2 ,,,' ?令Error: Reference source not found kkk=+h ,' ?Error: Reference source not found结好是Error: ReferenceK source not found中垂直面的反射波。 ,2πkh2πd=,1 又?,由结知,Error: Reference==ksinsinθθkh2λsource not found ,,' (其中Error: Reference source not?=2sindmθλkmk=hh ,,found) DE=ε 1.13 结结明,具有四面结性的晶～其介结常结结一结量介结常量,体称体数 εεδ= αβαβ0 ,, 结明, 由 Error: Reference source not foundDE=ε uuu,uuu,,,,''''' 各物理量在新坐结中,旧 pAD=DE=εEAE= uuu,uuu,,,,?+1'' (由于结操作称Error: ReferenceDAAEAAE==εεDE=εsource not found) '1?+ ?==εεεAAAA oA Error: Reference source not found是结X(a)结结结Error:90x 100 A=001Reference source not found是一结结的操作个称x 010? A Error: Reference source not found是结Y(b)结结结Error:y 001? oA=010Reference source not found也是一结结操作个称90y 100 '+ 将Error: Reference source not found代入 εε=AA 00ε 11 =0εεε2223 0?εε2333 '+ 再将Error: Reference source not found代入 εε=AA ε00 11 =00εε11 00ε11 1.14 若Error: Reference source not found的立方结如结所示～结构Error:Reference source not found原子的散射因子结Error: Reference source not found～Error: Reference source not found原子的散射因子结Error: Reference source not found～ F=?;a,求其何结因子几构hkl ;b,出;找h,k,l,晶面族的X光衍射强度分结在什结情下有 况 2 Ff+3AB I hkl2Ff? AB ff=(c)结 ～结衍射面指中些反射消失,结结出五数哪AB 结最结结的。 解,Error: Reference source not found结中～结胞构 中含有3个B原子～1个A原子。 ?++2πihxkxlx()jjj123 Error: Reference sourceFfe=,hklj not found 取Error: Reference source not foundError: Reference source not found 111111 AB0,0,0,,0,0,0,,Error: Reference source not found Error:() 222222 Reference source not found ?+?+?+ihkiklihlπππ()()()Fffeee=+++?Error: Reference source()hklAB not found Fff=+3当h+k与h+l～k+l均结偶结 数Error: ReferencehklABsource not found Fff=?当h+k～h+l～k+l其中结奇～一结偶结 两个数个数hklAB ff= 当Error: Reference source not found结有 ;0～0～1, AB ;0～1～0, ;1～0～0, ;0～1～1,;1～1～0,;1～0～1, 衍射面指的消光。数 1.15 在某立方晶系的结Error: Reference source not found射结粉末相中～结察 到的衍射角Error: Reference source not found有下列结系, 3:4:8:11:12:16:19:20 =sin:sin...sinθθθ128 222222222222=+++++++++++111200220113 222222222222++++++++++++222400331420 ;a,结定结结于结些衍射角的晶面的衍射面指～确数 ;b,结结立方晶是结立方、面立方结是心立方,体体 ad=Error: Reference source not found 又 Error: 解,hkl222hkl++ 2sindnθλ=Reference source not found hkl sinθλ222?=222 ??sinθnhnknl++()()()2a ++nhnknl()()() 3:4:8:11:12:16:19:20 =sin:sin...sinθθθ128 Error: Reference222222222222=+++++++++++111200220113 222222222222++++++++++++222400331420 source not found ? h k l = (1,1,1) (2,0,0) (2,2,0)…… ?结立方晶是面心立方体. 第二章 晶的结合体 2.1 结出NaCl型子晶中排斥结指的下列结系式,离体数 4418πε kR00 (SI结位)n=+12eα 102kNmRnm= =2.410/,0.281其中k结结模量～结已知体NaC晶的体～求0 NaCl的n=? 解,NaCl晶排斥结指的结系～结晶有体数体N元胞。个 2?eb?AB6α 结晶的能,体内UNN=(+)=[+]nnrrrr 2233其中,～结于NaCl结构～;结元胞的结,体A=αeB=6br=2Nr2r2 ? dr=6Nrdr dududrduNAnB1===?=0 rn2221+0dVdrdvNrdrNrrr660000 B1n?1r=?r? 在结平衡位置结,00An 222du1dun1e()?αkr由 ===22418Nrdrdr18rr0r000 44πε18kr4×18krk000? ;如取SI, =+1=+1nn22αeαe a=结于NaCl、CsCl、ZnS结构1.747、1.762、1.638 102r=0.281nm k=2.4×10N/m0 n?可求 2.2 结?e结荷的结结子相结排成一结晶格～结两离N结元胞～数B/Error: Referencesource not found结排斥结～Error: Reference source not found结正结子结离最短的平衡结。结明～当N有大结有,很 ;a,结德隆常数 Error: Reference source not found～α=2ln2 22ln21Ne UR=?1;b,结合能Error: Reference source not found;() 4πεRn 00 ;c,结结晶格结～当Error: Reference source not found),且Error: Reference source not found～结需做功Error: Reference source not found,其中 21ln2nN?()2Ce=Error: Reference source not found4πεR00 解,;a,一结原子结～正结子的距结离离a～相距结Error: Reference source not found的子结的相互作用结能,两个离 2qbur()=,+r=aR (R结结近结距结子结的相互作用结能离) ijjijnr4πrijij ，，2:,?NNqb11'',,==??,,Uur()???ijnnjj,,RaπεR224aij,,,j0j::，， 1'u=? 结子晶格的结德隆常 离数?jaj :,?，，11111,,==?+?+u2... ?,,,,a1234j，，:: 234xxx ln(1+)=?+?+...xx234 111ln2=1?+?+...令 x=1234 ? u=2ln2 du2n?1NqRln20=0(b) 利用平衡件 条 ? b=dRR0n 2n?1Nq2ln21R120uR()=?(1?) ? 0()=?2ln2(?)uRNqnRn0RnR 2dudu12uRuRRRRR=+?+?+L()()()() (c) 10002dRdR2RR=R00 由于外力做的功等于晶能的增量～外力做功的主结体内 21du2wuRuRRR=()()?=?() 0022dR0R 12()R=R1?δ()w=[ln2?n?1q]2NRδ?δ 将代入,002 晶被结结结位结度的结程中～外力做功的主结,体 2，，()w1n?1qln21=δ=cδ ,,22NR22δR,,00，， δ=δ 结结外力结Error: Reference source not found～外力晶与体(格)的e 形结成正比. F=α()2NRδF=α()2NRδ ～～Error: Reference source not found结0e0e 比例函数. 2NRδδ0ee WFdxNRNRd==αδδ22()e00 00 1122==22NRNRF()αδδ00ee2α 2NRδ 此结结子结被结结即离Error: Reference source not found的结程中外0e 力做功。 c()W=δ2NRδ Error: Reference source not found所以结结2NError:ee0e2 2[]()qln2n?1δeF=C=δReference source not found结外力 ee2R0 2.3 量子固体 在量子固体中～起主结作用的排斥能是原子的零点能～考结晶结Error:Reference source not found的一个即个氦粗略一结模型～每原子局限在一段结结L的结段上～每段内数的基结波函取结半波结结L的自由粒子波函数。;a, 结求每粒个子的零点振结能～ ;b,推结结持结结不结生膨结所需力的表式～达 ;c,在平衡结～结能所引致的膨结结向被范德瓦结斯相互作用所平衡～非常 粗略的结出最近结结的范德瓦结斯能结Error: Reference source not found～其中L以cm表示～求L的平衡结。 解,(a)根据量子力～学限制在L结段内的自由Error: Reference source ikxψ=Aenot found原子的波函数有形式 π22λππkk=L=== 又的波函数数结基结波函～所以基结波0λ22LL πix函数 Error: Reference source not found每个原子的Lψ=Ae0 零点结能也就是基结平均结能. L22:,?d,*ψψ,,dx00?2,,22mdx,::0T??== L28mL*ψψτd00?0 (b) 因零点结能会引起结段的膨结～结了保持结度结L的结段结～构必结增加力 22:,Td,,,, =?p=?=23,,dLdL8mL4mL:: UTUL=<>+ 有范德瓦结斯相互作用结～系结能量体() ??660 U;L,是范德瓦结斯能,ULerg= 1.610 2dU6h ?60==? 01.610 (c) 平衡结, 37dLmLL4 00L0 Error: Reference source not found Error: Reference source not found 4?804L=5.813×10cmError: Reference source not found Error:0 L=4.91AReference source not found的平衡结 0 第三章 晶格结力和晶的结性结学体学 3.1 在同结原子结成的一位点结中～若假结每个原子所受的作用力左右不同～其力 ββ>常如下结所示相结结化～且数Error: Reference source not found.结结12明,在结结的系结中～格波仍存在着声结支和光结支～其格波结率结 1 2 ka 2 4sinββ 11 +ββ22 12 = ?11ωError: Reference source not found 2M+ ()ββ 12 Vr 解,用Error: Reference source not found和Error: Reference source notss found分结表示第S初基原胞中原子相结平衡位置的位移个两个. && =???? MuuVuVββ()()sssss121? Error: Reference source not found &&MVVuVu=????ββ()() sssss121+ Error: Reference source not found i()ska?ωtu=ue 令Error: Reference source not found Error: References iskat?ω()source not found VVe=s 2?ika MueVωββββ?+++=0()1212 Error: Reference source? ?ika2 ++?+=euMccV0ββω() 1212 not found 2?ikaMeωββββ?++()1212?=0 ?ika2+?+eMββωββ()1212 222ika? Error: Reference source not foundMe?+=+ωββββ()()1212 +1ββ22212= ++2coskaωββββ1212MM 1 2ka 2 Error: Reference source not4sinββ12 + ββ122= ?11 2M+()ββ 12 found 3.2 具有结立方点结的某结结晶格～结原子的结量结两M～晶格常结数a～最近结原子结相 互作用的恢结力常结数c～假定原子垂直于点结平面作横振结～结结明,此二结系结 2Mckakaω=??22coscos的格波色散结系结()xy 解,只考结最近结作用第;l～m,原子个个受四原子的作用. ()l+1,m:c()u?u Error: Reference source not found l+1,ml,m ()l?1,m:c()u?uError: Reference source not foundl,ml?1,m ()l,m+1:c()u?u Error: Reference source not found l,m+1l,m ()l,m?1:c()u?uError: Reference source not foundl,ml,m?1 Error: Reference source not found 结方程,运 2dulmError:[]m=c()()u+u?2u+u+u?2ul+1,ml?1,ml,ml,m+1l,m?1l,m2dt Reference source not found uuilkamkat=+?expω 结 Error: Reference source not found()lmxy0 Error: Reference source not found ikaika?ikaika?2yyxxω=?+++?ceeee4() Error: Reference source not found =??22coscosckaka()xy 3.3 求, ;a,一结结原子点结振结的子结密度声Error: Reference source not found ρω～作结～并() ρω ;b,一结原子点结双声振结的子结密度Error: Reference source not() found～作结并. 解,一结结原子结, β1 =2sinqa Error: Reference source not found ω M2 ,L?=ρωω2//dqdq() (),2πs ;有个3n色散结系,Sn=13L 一结结原子结 S=1 L1?= ρω2()2π11β2cosaqaM22 Error: Reference source not L1β=1Mπaqacos2 found 一结原子结双: Error: Reference source not found 1 2 mMmM+41 22ωβ= ?11sinqa 2mM2mM+() 112 2 +mMmM41 2Error: Reference?=+?ωβ11sinqa +2mM2mM+() source not found 1 4 mMmM+41 2?=??11sinqaωβ ?2mM2mM+() Lddωω+??= +21/1/ρω() 2dqdqπ 3?LmMmMmM1414111?β24{1/{{1[1sin]2sincos}qaaqaqa=+? 22mM42222+mMmM++π()() 3?141411mMmMa?24+?? 1/{1[1sin]2sincos}qaqaqa242222mM+mM+() Error: Reference source not found3.4 结某三结晶光结子的体声色散结系结 2ωωqAq=?Error: Reference source not found～结结明～其子结密度结声()0 Error: Reference source not found 1V 2ωωωωω?<<,()0min03 22 4Aπ =>0,()ρωωω 0 0,<ωωmin 223 6πN 式中A, N结晶的原胞体数. =?ωω min0V Vdsc=ρω(),解,3 ω2π()sqsα Vc dsα3第支Error: Reference source not found格波的模式密度2π ωsqα sαError: Reference source not found其中Error: Reference source not found结第Error: Reference source not found支格波的等结面. 2ωωqAq=?又因结在q=0附近 Error: Reference source not found()0 Error: Reference source not found 等结面是一个球面. 又 =?=ωAqAq22Error: Reference source not foundq Error: Reference source not found 12Vωω?V()1c02c= =4qπ3/22Error: Reference source not foundds24AqA3π2π ωsqα 3.5 使用德拜近似结结同结原子所结成的下列系结的低比温结容结 CT ;a,在一结系结中～v 2CT ;b,在二结系结中～v ω=qv解,结于一结结结格子～按德拜模型,Error: Reference source not found 2dqLdqLLdωdL=== dError: Reference source not found范结包含内2VπππError: Reference source not found ωL0DdNωω== Error: Reference source not found ;N结原子数() 0a 目, π?=V Error: Reference source not found 比结容,ω0a 2h/KTωBωeDdωω ()hω0Ck= VB2 0h/KTωBKT Be?1() 2h/KTωB ωLeh0 ωError: Reference source not found=kdω B 2 0h/KTBωVKT π Be?1() 22x/TΘ2TkexdxDB=2 0xhVe?1π() x2,exωhωx ? 01Θ=x=D 在高温结,Error: Reference 2xkKTe?1B()B source not found Error: Reference source not found Error: Reference source not found Error: Reference source not found LCkNk==VBBa 低温结 Θ/T?? Error: Reference source not found D x2?2 ex?22xxnx=?=xeexne1(), Error: Reference source not found2=n1xe?1() x2 exdx 1π?nx2===nexdx2 Error: Reference source not22 n=10xn3e?1() 22πTKBfound Error: Reference source not foundC=Vh3V sdlω=ρω(),结于二结结结格子,Error: Reference source not2 qω2sπ()qs found ω=vqError: Reference source not found ～所以格波等结;能,结结结. Error: Reference source not found SdlSqsωπω2= ==ρω()222 VV2π22Vππ()() 二结介结有两支格波,一支声学波,一支光波学. sωD==ωρω()()Error: Reference source not found 2Vπp 211=+222VVVpLτ Error: Reference source not found 2ωωρωωωhd()ShωmmEd==ω2h/KT ωB00h/KT2ωBe?1Ve?1π()p ωωmmSωρωωωdNd==2Error: Reference source not found ()2 Vπ00p 12N ?=ωπ4Vmp S 2h/kTωBω sedhωωωmCk= VB22 0h/kTωBVkTπpB e?1()Error: Reference source not found 2x3Θ/TkTsexdxD B= 22 0xVh πpe?1() ,ωmΘ= Error: Reference source not found Error: ReferenceDkBsource not found x当温度结高结,Error: Reference source not foundex +1 2x3/TΘskkTexdxD BBC=V 22 0xπVh pe?1() 2Error: Reference source not found skkTΘ BBD= 22VTh2 πp 2=NkB x3 ex1?nx3==nexdx663ς() 23 00xn当温度结低结,Error: Referencenn11==e?1() source not found 2CAT=Error: Reference source not found Error: Reference source notV 363ςSK()BA=found Error: Reference source not found 22hVπp 323.6 结某特殊二结系结子结声率Error: Reference source not found ,结结ωKAq=() 明～此系结的 7;a,平均振结能量正比于Error: Reference source not found～3T 4;b,子声比结容及结正比于. 3T dd/µ+1C=CT解,3.7结中 ?UµVT 3µ= 结于二结系结 d=22 44C Error: Reference source not found ? 同理结,S?V33TT d27+1+1µ Error: Reference source not found ?U3/23TTT== µ3.7 结d结结结晶格中～结率Error: Reference source not found与成正比～结结明q d?1µ;a,结正模;子结,密度声Error: Reference source not=Bρωω() found～ dµ;b,比结容Error: Reference source not found.B、C结常数. C=CTv µω=kq解,Error: Reference source not found Error: Reference source ωdµ-1ddd??1'1 qnot found ω=qkdKdqcqω==dq dSdρω ()S Error: Reference source not found Error: dddq/ωSd Reference source not found结d结空结等结球面. d?1qd?µρω qError: Reference source not found Error: Reference()?1µq 1source not found Error: Reference source not found µq ω d?1µError: Reference source not foundρωω () d?1 µdEddhωωωC==Vh/kT ωBdTdte?10 d µ dhhωωd+1''d µcKT ()ωDBKTKT　　　　 BBdT=dh ω0KTBµhe?1 d2 µ hhdωωω=K B2 h/KTBKTω Be?10() d?1'd?1dz(q)=cqdq=g(ω)dωg(ω)=cω ωhωD'1d?Ucd=ωω/kTh ωB0e?1 d hhωωd '1d+kTkTckT()ωD BBB=hd ω0hkTBe?1 'd,ωxc(kT)xdxDB=x令 = 当结T?0U?dx0kTB,e?1 dd+1CT UT v d?1结结 '' µgc()ωω= d?1ωhωD''µUcd=ωωh/kTϖ B0e?1 d µ hhωωdd+1 ''µckTkTkT()ωDB BB=dh/kT Bω0e?1µh d U d/µ+1µCT= 故在低温结 V UT T V ωω>3.8 求在一结结原子结中～Error: Reference source not found;截止结率,m αω格波的阻尼系数Error: Reference source not found与Error: Reference source not found的结系. ωα=2arcosh ωm iqnaqt?ω () 解, 结原子结, Error: Reference source not foundUAe=n qBZ 1 1β Error: Reference source not found qqa=2sinω()M2 β =2ωmM 1ω>ωsin1qa> 当结 Error: Reference source not found～q必定结结m2 qqiq=+数～令12 ω11111=+=+sinsincoshcossinhqiqaqaarqaiqaqa() Error:12121222222ωm Reference source not found 111 qah= π?=cos0qa Error: Reference source not found 1 1222 12ππ = = qhKError: Reference source not found1n 2aa πω2πqiar=+coshq=将结入1aaωam πω2iiarnat+?coshω aaω m UAe=n ω?2coshnariit?ωπωm Error: Reference source not found =Aeee innait??πω=Aeee nnaitω=?Aee1() ω2=arcshα Error: Reference source not found 结指数减衰因子.ωm p2 2UU??1e()()nnp?f ? 13.9 Grneüisen常量.npn?,2papa () ;a,结明结率结Error: Reference source not found的子模的声自由能结 hωKTln2sinh～ BKT2b ;b,如果Error: Reference source not found是结的相结结化～结晶的体体自由 能可以结写 , hωq()1 2 FTBKT?=?+,ln2sinh() ,B KT22qb , qω其中BError: Reference source not found结的结性模量～体假定与体结结系结()dqω()γ=?γ?Error: Reference source not found～Error: Reference source()qωnot found结Grneüisen常量～如果结结Error: Reference source not found模与Error: Reference source not found无结～结明～当 1q(),ω()B?=qcoth[]结～F结Error: Reference source not found结极小～,?γωq22KTB ?=UTB/γ～ 并将它写结明利用结能密度～可结() hωln θD=θ=?;c,根据Debye结明, .其中(Error: Reference source notγKlnV B found 解,考结结率结Error: Reference source not found的子模～声数配分函结 1 +nhω 2 ?KTBZe=,n=0 hhh2ωωω??? 2KTKTKTBBB=+++eee1... hω? KTBe=hω? KTB1?e 1=hh?ωω22KTKTBBee? 自由能, Error: Reference source not found :,,ω,,=?=FKTlnzKTln2sinhBB,,2KTB:: hωK=+FrTErKT,ln2sinh 晶的体自由能结, ()() ,B2KTK B 若晶结体体改结结Error: Reference source not found结δr hωδrr+() KFrrTErrKT+=++,ln2sinhδδError: ()() ,Bk=02KTB Reference source not found 2 1 E2ErrErr+=+δδ()()() 22 r 0 12=+?ErB()2 2 Edr2Br=?= 结结性模量体. 2 rr 0 Error: Reference source not found hωδrr+()1K2FTBKT?=?+,ln2sinhError: Reference source not() ,BK22KTB found ωk+=+rrrdrωδω()()kk r rr ωδ k=+r()ωωkk rr ωk =??ωγωφkkk lnr ωω KK=?=?γ其中Error: Reference source not found结GrneüisenK rrlnω K 常数 γγγ= 假定与k无结 KK hωδrr+() Fk=?+BKTln2sinh ,B ? ?2KTKB +rr h()1ωδωkk=?+Bhcoth ,22KT ?K B =0 Error: Reference source not found +ωδrr ()hhωKKB=?cothError: Reference source not found 其中 ,K22KT ? B +ωδrr()K=γωK ? 1hωK?=Bhcothγω Error: Reference source not found ,KK22KT B 平均结能, F FT 2 UTFTT=?=?() TT r V hω 2k=?Tkln2sinh ,B TKT2K B h1ωk=hcothω ,k22KTK B ?=UTB/ωγ 假定与T无结 ()K EdEhω K=?=??PKTln2sinh 由物结方程 ,B k 2rdrrKT T B Error: Reference source not found利用Deby近似～第二结化结,将 ω hωωD? KTDdln2sinhωω()B θ 2KTrω B ω qNhhDωω2=? KTdcoth ωω B2 θ22KTKTr ωBBD Dω qNhhln3ωω=?cothd ωω3 22lnrKTr DB ω0 hωhω lnωKKX==θ=? 令, , 上式化结, γKTK lnrBB 3θqTxγ 3T NKTxdxcothB 022rθ Error: Reference source not found 平均结能, hω1k=UThcothω() ,K22KTK B 3θqTx 3T=NKTxdxcothB 022 θ UT()dE ?=?+Pγ drr UT()=+Pγ0r =ωωError: Reference source not found 取结D lnlnωθ=?=?结正结;Grneüisen常量,γ lnlnrr 3.10 科恩;Kohn,反常. 假定作用在l平面上结的力结方程 FCUU=?(),LPPss+ P C 其中晶面结的力常量结P sinKPa0CA= Error: Reference source not foundPPa K结常数Error: Reference source not found～p取遍所有整 式中A和0 数.在金中可能有结结形式属.利用此式和晶格振结方程结明其色散结系结 221cosωqCqpa=?()()Error: Reference source not found结算,PMP>= 22 ωq ωq()()2qK=ωq的表式达.结明当结～结无结大～结结并Error:()0 q qReference source not found的结化情况. &&CmUCUU=? 解,若力常结数代入Error: Reference source(),PsPpss+P not found iqnat?ω() 令,Error: Reference source not found 得,UAe=s 22ω=?CPKa1cos(),PMP0> sinPKa20=?APKa1cos(),MPaP>0 2?2Aω=sinpka?sinpka Error: Reference source not found 0?2Mkp>0? 2?ω2A2k=k当结 右结结散=sinpka?0?0?kMp=1 2uu, ω2ωKωKKK= 结明子声色散结系或曲结在结斜率出结 ,即() ()0 K k了垂直的正切结化～也就是子声色散结系在曲结Error: Reference0 source not found结有曲折;kink,此即Kohn反常 3.11 结子模声. 结有等结量而结荷交替结的一结子结～第号离l子的结荷结个离Error: Reference source not found.原子结的结结结结结之和,;两献1,最近结子结的短程结性相离 互作用～力常量结Error: Reference source not found～以及;2,所有离子结的结结相互作用. 2el(a)结明结结相互作用结原子的力常量的结结献Error: Reference()C=2?1lc33la source not found～其中a是最近结平衡距离. (b)由晶格振结方程推结下列一般的子声色散结系, 22ωqCqpa=?1cos()() ,pMp>0 2lω1 4β?232=+??sin11cosqaqlalσ= 结明,色散结系可结写式中ω()(),m2l=12Mωm 2eσ=而 3βα qa=π(c)结明在布里结渊区界结～若Error: Reference source notσ>0.475 2ς4/7ς()3ωqfound或结～结是结的;不结定模,～结里是Riemann-() ?1Zeta函数.结而结明～如果Error: Reference source notσ>=2ln20.721 found～结结于小的qa声虚数速结.所以若Error:0.4750.721<<σReference source not found～结于在Error: Reference source not 2ωqfound结的某结区内个qa～结结零～因而晶格不结定.注意～子结不声() 是原子晶格型的～因结任一子其近结的相互作用其双离与与离他子相同.解,结子模 声 ;a,结子结离沿水平方向～第n子个离右端的第n+p个离与子第n 个离子结的结结力 npn+2??11e()()f=?Error: Reference source notnpn+,2 paUU+?()npn+ UUpa?<kkγ()10xnot found ()Ψ=Ψ'?kk00EE?,0k '''=V(n) Error: Reference source not found ()k=k '''=0Error: Reference source not found ()k?k ,, 以I j 表示结位矢量～ Error: Reference source not found表示倒格矢bb12 ,,,,,,,,2π()=+=+, Error: Reference source notGGbGbgbgbrxiyj=+11221122a found Error: Reference source not found 结整数.晶结能体 22ππ UxyUxy,4coscos=?() aa 2222ππππixixiyiy?? iG1,1()σσσσUU=?=?++UrUeeeee其中Error:() G1,1,()G1,1() Reference source not found UU===L0而其他结能结氏系 数Error: Reference source not foundGG1,02,0()() 结结基本方程:Error: Reference source not found λε?+?=CkUGkG0()()()结结,kGG λε?+?+?+?+CkUCkGUCkGUCkG()()()()kG1,11,11,1()()()()GG1,11,11,1()()() UCkG?=0()G1,11,1()() ππ ,Error: ReferenceError: Reference source not found求布里角结渊区 aa 111 kGG==,1,1source not found 即Error: Reference source not found() 222 结的能隙～可利用结平面波近双似, ikGr?()ikr?=+?CkeCkGeError: Reference source not found ()() 11kGkG==?1,1,1,1当Error: Reference source not found结依次有Error:()()22 1kGG?=?1,11,1Reference source not found ()()2 1kGG?=1,11,1Error: Reference source not found 而其的它()()2 kGG?>1,11,1Error: Reference source not found所以在结平面波近双似下()()只有, 1111 CGCkGCGCGCkGCG1,1,1,11,11,1,1,11,1?=??=()()()()()()()() 2222 11 λε???=CGUCG1,11,10()() 1 1,1G()22 2 11 CGUCG???=1,11,10()()λε 1 1,1?G()22 2 λεµ??11,1G()2=0??µλε11,1?G()2 2222hh1π 因结Error: Reference source not====1,1Gλλλ()112 1,11,1GG?()()22mma 22 found 22由行列式,Error: Reference source not found λε??=U0() 22hπError: Reference source not found= = UUελ2ma 4.8 平面正六角形晶格;如结,六角形结结的结距是两个a～基矢结 ,,,13 Error: Reference source not found aaiaj=+122 ,,,13Error: Reference source not foundaaiaj=?+222 结出此晶的第一、二、三布里画体渊区. ,,,,,aa,解,取结位矢量垂直Error: Reference source not found ak=k123 ,,,32Error: Reference source not found ?==aaaa?()1232 ,,,,,2πaa ()22ππ23bij==+Error: Reference source not found 1?a3a ,,,,,2aa π()22ππ31bij==?+ Error: Reference source not found2?a3a ,,,2πaa ()12 Error: Reference source not foundbk==2π3? ,, 在Error: Reference source not found、平面结一倒格点结原点～原点内bb12 ,,,, +bbbb、、最近结倒格矢有6个 正六结形结第一布里渊区.()1212 4.9 用结束结方法结出心立方晶体体s结结子的能结: ,kakakayxz Error: Reference source notEE8coscoscoskJJ=??()s01222 found kkk==0Ek 结出画沿方向Error: Reference source not found,和()()xyzx VkError: Reference source not found的曲结.()x kakakayαtxz解:结束结s结结子能结 Error: ReferenceCJEE8coscoscos=??ssss222source not found 用结束结方法～只结其最近结格点作用结 ,,,,iKRαtnEEKCe=?? Error: Reference source not found 是R(),sssn 最近结格点 aaa 0,0,0,, 取参考点的坐结Error: Reference source not found() 222 代入上式 Error: Reference source not found ,,,iKR αtnEKECJe=??(),ssssn aaaa()()()()ikkkikkkikkkikkk+++??+?++ xyzxyzxyzxyz2222tαECJeeee=??+++sss aaaa()()()()ikkkikkkikkkikkkxyzxyzxyzxyz ?+?+???+???2222Jeeee++++s aa?+??ikkikk ()()()()aakkxyxyzz22ikkikkkkxyxy2coscoscoscosaeaea22t++zz+? ECJeaeαsss2222=??+ aakaikik kaα?xx ytz224coscosECJee=??+sss 22 kakakaαytxz8coscoscosECJsss=?? 222 31,1,1在方向上Error: Reference source not found[]kkkk===xxz3 πkkk=== 在第一布里结渊区界,Error: Reference source notxxza found 33EE8cos=?JkaError: Reference source not found s0s 6 kkk===0EError: Reference source not found 最小结结xxzs?===kkk0Error: Reference source not found是能结底xxz Error: Reference source not found 22hh???mmm====xxyyzz22Ja2 Ess2 KxK=0x 222πππ ,0,0,0,,0,0,0,在结界Error: Reference source aaa not found是能结结 2h???mmm===?Error: Reference source not found xxyyzz2Ja2s 其交它数会叉结的倒也结零。 4.10 用结束结方法结出面心立方晶体s结结子能结, ,kaka kakakakayyxxzzEKE4coscoscoscoscoscos=??++JJErro () s01222222 r: Reference source not found 并求能结底部的有效结量. uu,uu,uu,uu,u,iKRiKRαtnnEKE=??CJee解,由Error: Reference source not() ssssn uu,Rfound (结最近结)n 0,0,0以结坐结原点有12最近结,个() aaaaaa ,,0,,0,,0,, Error: Reference source not 222222 found aaaa,ikkikkikkikk+?+??? ()()()()xyxyxyxyαt2222EkECJeeee=??+++?() ssss aaaaaaaaikkikkikkikkikkikkikkikk+?+???+?+??? ()()()()()()()()xzxzxzxzyzyzyzyz22222222JeeeeJeeee+++?+++ ss aa tα =??++?ECJkkkk2coscos?()()sssxyxy 22 aaaa JkkkkJkkkk++??++?2coscos2coscos()()()()sxzxzsyzyz 2222 kaka kakakakayytαxxzz=?? + + ECJ4coscoscoscoscoscossss 222222 , EKK0,0,0能结底即最小结()()s 22hh???mmm====xxyyzz22Ja E Error: Reference source not found s2 KxK=0x 1xna??ααtα?αxnae?=()s其交它叉结结零.NVXAxna=??δ()(),n1= 22hd4.11 结一结晶晶格常结体数a～系结的哈密结量Error:HVX=?+()22mdxReference source not found～其中 VXAxla=??δ()() Error: Reference source not found～若已知孤立,l 原子的结和波函数结 122αh??αxla2 VAxlaeE=??==?,,δ?α()aaa2m 结用结束结近似求s结结子的 ;a,能结公式～;b,能结结度～;c,结底有效结量. NVXAxna=??δ解,由Error: Reference source not found()(),n=1 δxna? Error: Reference source not found结Error: Reference source() not found～孤立原子中s结结子的波函数 1xna??αtαα Error: Reference source not found?αxnae?=()s uu,uu,u,iKRαtnEKE=??CJe Error: Reference source not found Error:(),ssss Reference source not found结最近结 Error: Reference source not found ?atatat CxVXVXXdX=????()()()()sss Na ' 取等格点号～结nax= N* atat'''=????+??CxnaAnaAxnaxnadx?δδ?()()()(),sss n=1 Na N* ''atat=?????xnaAxnaxnadx()?δ?()(),ss ' nn Na =0 *atat''' JxnaAxnaAxnaaxnaadx=????+?????δδ?()()()(),sss Na 8Natat', =??????xnaAxnaxnaadx()()?δ?()',ss nn ErrorNa ''xnaxnaa?????αα' =???eAxnaedx()αδ Na ?aα=Aeα : Reference source not found 上式结分只取了右结的最近结～取左结最近结也相同. ,,iKRiKaiKa?n2coseeeKa=+=又 Error: Reference source not found ;由,n 于等点号两个左右最近结, ααta?EKAeKa=??α2cos Error: Reference source not found()s πK= Error: Reference source not found 结能最大 a π ta?ααEEAe=+2αError: Reference source not founds a 2πK= Error: Reference source not found 结能最小 a 2π ta?ααEEAe=?2αError: Reference source not founds a 2ππ ?αa?=EEAe4α结结 Error: Reference source not found aa 2=*m,xx?2E 结结有效结量 Error: Reference source not found 结结 2?kπxk=a 2=*m,xx2?E Error: Reference source not found 结底2?k2πxk=a 4.12 结由结束结近似结明晶格常结数a的结结一结晶中～第体l格位上s结子的概率幅 Error: Reference source not found 结足方程, &iCtACtBCtCth=??()()()()llll?+11 AEJ=?BJ= 式中Error: Reference source not found～Error:s01 EJReference source not found～是孤立原子s结道的能量～是晶结劈裂～s0 J是最近结交结分叠.假定一结中晶结中原子结结数N～结求,1 , EK=?;,a结子的能量波矢结系与Error: Reference source not found() ;b,能结结度和结结空穴及结底结子的有效结量～ ;,c结Error: Reference source not found～求能结结子的结密度A=0 ρE=?Error: Reference source not found() ;,d假定原子有一价结子～结求个Error: Reference source not found结T=0 0E的结米子能Error: Reference source not found.F 解,结第n格点上结子的个几率振幅结, E ?iKnat hError: Reference source not found 第Error: Referencen?1 CCe=n0 source not found和第Error: Reference source not found格点上个n+1 E ??iKnat1() Error: Reference source not found h CCe=n?10 E iKnat+?1() h CCe=n0 将以上三式代入Error: Reference source not found &iCACBCBCh=?? 得,nnnn?+11 E ?ikaikaiiABeBeh?=??Error: Reference source not found , h Error: Reference source not found. 结结子能量EABka=?2cos Error: Reference source not found 是结子能结底～在能结底结子能量的有k=0 效结量 22hh?m==2Ba2Error: Reference source not found E 2 KxK=0 22hh?m==?2πBa2 EK= Error: Reference source not found 结能结结 2a KπxK= 2Error: Reference source not found 2h*结结空穴有效结量 Error: Reference source not found m=2Ba Na?2dk能量结波矢结,区数Error: Reference source not found EEdE~+π2 NaNa21dzdkdE= = 22dE2ππ dk 21NaError: Reference source not foundError:= dE2sinBakaπ 21N=dE22π4BAE??() Reference source not found Error: Reference source not found 结能结密度,A=0 dZN21 NE==()Error: Reference source not found 22dEπ 4BE?A=0 Error: Reference source not found 晶有体NError: Reference source not found结子～在结结零度结都分布在结个米能及以下～采用Error: ReferenceN=0 source not found结的能结密度 EFNNEdE=() 0 EN1F=dE 20BπE 1? 2B 1=dx 21?x ?1=sinx 00 2EπE?1FF?=sin0Error: Reference source not found sin= π2B22B 0EB=2Error: Reference source not found F 2222, KKhKyxzEK=++4.13 某晶中结子的等能面是结体球面Error: () 2mmm123 Reference source not found～求能量Error: Reference source not found 之结的结结状数.EEdE~+ 2222 KKhKyxzE=++解,由,Error: Reference source not found 得, 2mmm123 222KKK312++=1 Error: Reference source not found 222mEmEmE112233222hhh 222xyz Error: Reference source not found 等能面结成的结球++=1222abc 体结, 31424π22 τπ=2mmmEdEdmmmEdE=2τ12312322hh3 EEdE + Error: Reference source not found 在能量结区Error:()Reference source not found结子结结内数状数目 1VVcc2dZdmmmEdE==22τ Error: Reference source not found123323hπ2π() 1VdZc2 结子能结密度,Error: Reference sourceNEmmmE==2()12323hdEπ not found 222222uu,hKhhKK312EK=++ Error: Reference source not found ()222mmm123 ,,,, EEE =++EKkkk()k123 kkk123 222,,,hkhhkk312 Error: Reference source not found=++kkk123mmm123,,=vk() u,uu,uu,uu, BBKKK=++αβγError: Reference source not found 磁感结强度()123,,,dk代入结子结方程,运,=?qv×B dt,,, 结用, k×k=k 结入结方程, 运123 uu,uu,uu,uu,uu,uu,uuu, KdKKK312qKKKKKK=?++ ++ βαβ Error: () 123123γdtmmm123 Reference source not found KdKK312=??qBγβ Error: Reference source not found dtmm23 KdKdKKKK332112=??qBqBαγ=??βαError: Reference source not dtmmdtmm31 12 found Error: Reference source not found 0itω0itωKKe=KKe= 令 Error: Reference source not found 1122 0itωKKe=33 γβqBqB000iKKK+?=0ω ,即Error: Reference source not found123mm23 qBqBγγ000iKKK+?=0ω Error: Reference source not found231mm31 qBqBβα000iKKK+?=0ω Error: Reference source not found312mm12 由系数行列式结零 Error: Reference source not found γγqBqB?iωmm23 qBqBγα?=i0ωmm13 qBqBβα?iωmm12 222 qBqBqB()()() 2222??+++=iωωαγβ0 Error: Reference sourceω=0 mmmmmm231213 not found无意结 12 111222 Error: Reference source not found =++qBωαγβ mmmmmm231213 12qB mmm?123ω= m=? 222ωmmmαβγ++123 4.14 一结金的属peierls失结;结结基泰结《固体物理结结》10.7式, 2h2k 考结一结金结子结属气米波矢结～结足自由结子能结如果一结晶格由结Ekk()=F2m cos2?kx子相互作用结生的气周期形结结～其结性能可表示结F 11222VxAkx()2cos2=?cos2Eckxc=?< ?结形结同结使结子结在一个周期结结FF结24 ()2cos2VxAkx=?中F 结结算, ;a,在结周期结作用下结子在附近的能结～ ;b,结系结的结子能量和形结能求结～求出系结的最低能量所结结的型结～ 222?hkcAππ/422FhkcmAπ/41>>;c,在结～形结的表式结达～??=?2/hkmAeFF k 解,考结一一结金～在结结零度下其中结子个属充结所有结结结道直到波矢～peierlsF 2Gk=提出结结一结性金在波矢结个属的周期性结点结下是不结定的～结形结在结静个米F 面上结生能隙～使能隙下面的能量降低～形结结结增大～直到被结性能的增加所限止 d(E)0E+=平衡形结由确定?结结d? ()2cos2VxAkx?假定使结结子感受到的点结位结比倒于形结,F 1222222hk hhk222222根据并定结 x=kVkmAε=+ +?4/2h()()k kFFm22mm dε?222khkhkk=FF1 x=x=d?F222xxA+?mm()Fk 1?结位结度中结道目数结～可得,π 2kkdE dε22Adk?FF结k==dk 1 00d??dππ22 2xxA+?()Fk x kkxdxF ?1FFF==sinh 1 0xxA? 222 FF2xA+?() 22 1hk221?FcAmAk?+=2/sinh0h?π平衡方程化结,() F2mA? 222222 hhkkc?π?hkcπFFF=sinh如果 相结于能量极小的由?>>1 22mAmA?44mA 222 2hk?hkcmAπ/4FFAe?? m 第五章 金结子结属 5.1 结一二结个气数自由结子系结～每结位面结中的结子结n～结求出结系结的;a,能结密度 N;E,～ 2 nhETKT=?lnexp1;b,结米能;化式, 学Error: Reference() FB4πmKT B source not found mSNE=解,二结结子能气太密度 Error: Reference source not found()2πh 结结位面结金的结子结,属数 1nNEfEdE=()() 0s Error: Reference source not found mdE=2 EEKT?/()FB0πhe+1 Error: Reference source not found 令,Error: Reference source EE?Fx= not found KTB mKTdxBn=2x ?EKT/FBπhe+1 ?x mKTedxB=2?x ?EKT/FBhe+1π Error: Reference source not found mKT?xB=?+ln1e()2?EKT/FBhπ EF mKTKTBB=+ln1e 2h π 2EnπhF Error: Reference source not found Error: ReferenceKTmKTBB1+=ee 2nπh mKTB ?=?EKTeln1source not found Error: Reference source not foundFB ,,,*E=(E,E,E)5.2 结阻尼结结～结结明,当～B=(0.0.B)结结结率公式结?mv/τxyz JE?10ωτxxc σ*2*JE=?10ω=eB/mωτ其中～ σ=neτ/mcycy 2+1()ωτ c2 JE001+()ωτ zzc ,,,,d:,1m+v=?e()E+v×B结明,由,,ττd:: :d1:,()mveE+Bv=?+,,xxy,ττd,::在x,y平面,, d1:,,()mve+EBv=??,,yyx,dττ::: τeE?:xωτvv=?xcy,m,Error: Reference source not found , τeE?y,vωτv=+ycx,m: d:,1m+v=?eE在z方向上,,,zzττd:: dvz在恒定结结的定结情,况 Error: Reference source not found =0dτ eE?τzv=zm 2,neτJ=?nev=Ezzm J=?nevJ=?nevError: Reference source not found yyxxError: Reference source not found JE10?ωτxxc σJE=?10ωτ ycy 21+()ωτ c2 JE001+()ωτ zzc ,5.3 Error: Reference source not found结子漂移速度Error: Reference sourceV dVV ?meE+=?not found的方程Error: Reference source not found结明,结 dtτ ω率结Error: Reference source not found的结结率结 1+itω=0σωσ()() Error: Reference source not found～其中Error:21+tω() 2στ0/=?nemReference source not found () ,, dVrdme+=?ε结明,结子源移速度,Error: Reference source not found dtτ 1+itω=0σωσ Error: Reference source not found()()21+tω() itωεε=e 结交结结结,Error: Reference source not found0 Error: Reference source not found Error: Reference source not found ,, dVreitωdd?+=?meε 0dtmτ itω结上式特解结,Error: Reference source not foundAe τεeeεA00?=?AiA?+=? Error: Reference source notω+mit1ω()mτ found ,,tdVV,?dd Error:Error: Reference source not found 0+=τ? Bedtτ ,Reference source not found 结的通解Vd t,,?eτεitω0τ?= ?VBeedmit1+ω() t??当达结子到结定结, ,eτεitω0Ve=?Error: Reference source not found dmit1+ω() 2itω,,neeτε0JneV=?==σωε()Error: Reference source not found dmit1+ω() ?1itω=0σωσError: Reference source not found 其中,()()2+1tω() 2neτError: Reference source not found0=σ()m 1+itω?itω=0σωσεε=eError: Reference source not found ()()021+tω() 5.4 在低温体与温下结结结出某结结晶的比结容度的结系 3/23/2C/T?T结一直结～斜率结B截距结A～如结v 所示 C;a,出写温低下与T的结系～v ;b,若已知直结的斜率部分来声献源于子结比结容的结～ θ求B德与温拜度的结系～D ;c,结截距部分来献估源于某波色子结比结容的结～结结结准粒子的色散结系 µµ=?ω?q 中的 333 解, Error: Reference source not found22C/T+AC=BT+ATvv 34:,12πNKTB,,= 又根据德拜模型～在低温下Cv,,5ΘD:: 412πNK1B=B Error: Reference source not found 3Θ5D 1:,412NK3πB,,Θ=D,,5B:: 3又来声献自子结比结容的结2AT d3µµ如3.7结在d结晶格中～结截距部分比结容 qω2CT ATv µ=2又因结三结晶格 Error: Reference source not found Error:d=3 2ω?qReference source not found 目 结 第一章 晶的结及其结性体构称...........................................................................................1第二章 晶的结合体.........................................................................................................10第三章 晶格结力和晶的结性结学体学................................................................................14第四章 能结结..................................................................................................................29第五章 金结子结属...........................................................................................................47 致 结 结结就像被不结结的结～断你它趟无结在干什结都感结到的流逝～结结结的河流不知不结我结的大的生学即将学活已结束。在大的四年中无结是结结知结结是结人生价结的结结都得到大很提高。 首先感结培结了我结四年的母校伊犁——学学与学结范院～再次感结物理科技结院各位结结及老结的大力支持～感结结结你学学我结提供了结良的结结境～感结院各位老结四年来结我结的栽培～使我结结有了一定的结结知结和技能。 　　本次结文是在结新结老结的悉心指结下完成的～结老结结学渊教博～理结功底深厚～结学真尽教学结结结。在完成结篇结文的结程中～管他工作非常繁忙～但结是结予了我耐心的指结～结结文初稿结行了结结结～结结真并宝文初稿提出了十分结的修改意结～在我的结文的撰写很结程中～老结花结了多的结结和精力结行指结。在此～我结向我的指结老结结新结老结致以我结结的结。 感结所有老结、同、学帮朋友、及所有结心我和结我提供助的人。愿他结接受我最结结的结意。