9-弹性系数张量

unitelastic這節我們介紹彈性係數張量，我們將以Si來做示範。首先，Import—個Si的晶體然後先進行GeometryOptimization的計算，這是為了找到最低總能

計算完最低總能之後，接著計算ElasticConstants+oAlCA|TEP^1J+口AlCASTEPCeo^Qpt+QAlfeASTEPGeomOpt^)4□Alj^iiCASTEPGeomOpt+QA1_U1tisiCASTEPG閃岭t-a.Si-CASTEPGeomOpt+DSiCASTEPCij…磁宙-vCalculation!卜“鶴獄;塗d®Status.txtIk-.-SiEnergies.xc:d囱iSiTiaijeet^r^.xtdSparam.0.$if亂tep驚Al.xsd•4瓠駅再來就可以開始分析ElasticConstants,按下計算，即可得到彈性係數張量Corre1ationcoeff:0.999737Stressintercept:-0.033706SumEaryofclasticconst目ntsid1jCij(GPa)111163.13775+7-0.302444S0.79260+7-L3097126L58560十/-0.2S8ElasticStiffne&&1Lon5tant&Cij(GP韵163.137756L5856D6L5S56OO.OOODD0.000000.0000061.5呂560163.137756L5S56O0.000000.000000.000006L5S5606L5856D163J3775O.OOODD0.000000.00000比較由書中所查資料，可見所算結果相當吻合。291GeneralTlteorvofLinearElasiitiiy291ElementAr(Mi)KJA-gAuCi178Ki|CuC(diainiMKb民|Ciclurukipcd)EGe(n^>prdJOlsNh}|GeU>4jpa1.HK°Gii■He4<<>•!K.24urn'/molejKfltl5KaCn(GPw•a(GPj)G:(GPatElememCn(GPa)Cw(GPa»10828362；Li(!«K»HT*2.7705*S137Mo4-5911112345,392iVa7.5943019042.3⑹NcibK^l.fiZQ.932472.M1.48Ni2471221612&Nb2452S.4346IIX)66O1514K)2.M)0.27516975.3122Pd22471.6KUO55()170Pl4776.5230117135Rb2.96IM12967.148Si(uncJmptxl)165沙.212R.X65547.7Sigtkpoi.m’A”162.27R.7118.065339.0Sr14.75.74002350.010850.0197Ta262&260.0311O.O2I7（H）技1Th76466()02702ZW5171571.71I.S8i15V23U4>.22出1.35L60XeriiftK)2.9«i.4848卅14.841.45(GPa>TiT16X633TftMe12.1.Elasticconstantsforcubiccrystals0.851551322.O6E25lrs4lr2(>3^jBtscrll»airheCauchycelutionf第=ChisbadlyvioUurdforulnu^taUcniriv^Sourer;■doltandBdrnsteiu<NwSeriv^hvpI.I】・、remaininvarianluntterinfinitesimalvariationsaboutthezaxisrAnaltenu-ix(udemandthetreeenergytoremainimarisintdtkter45roinlions.tbouitheInthisgse.thtstniintensorc•仃j(r)transformsinto(产)・wheree^(r]站(1220a)孑=R7andK=丄(110心\00>/2itu(ebq・(12.20.)intoEq.11工14).sublracilhefreeenergyotthetotaled

fromthatMlheunrotatedstate,andckinanjthutth.re^ukvanish<Prohkm

cafT\mgout(heniirtnxmultipliuiiion^iindxomealgebra,lheresultis0(teCyiyTCrrnr-(总丹一女C_Cw)(怙屮2<罗一<xc)(12-21