清华大学-蛋白质晶体学课件-6

1.-Fe为立方系晶体，点阵常数为a=2.866Å,如果用波长为2.2909Å的X光照射，求（110，（200）和（211）面的掠射角？2.用波长为1.54Å的X射线，照射点阵常数为a=3.61Å的Cu，试用Ewald作图法求（200）面的角。空间平面间距(晶面间距)电子密度函数计算公式FourierSynthesisofBoxcarFunctionBoxcarfunctionPeriodicBoxcarCanthisfunctionbereproducedwithcosinewaves?k=1.OnecycleperperiodA1·cos(2kx+1)k=1Ak·cos(2kx+k)k=11k=2.TwocyclesperperiodA2·cos(2kx+2)k=2Ak·cos(2kx+k)k=12k=3.ThreecyclesperperiodA3·cos(2kx+3)k=3Ak·cos(2kx+k)k=13Ak·cos(2kx+k)NFourierSynthesis.NCyclesA3·cos(2kx+3)k=3k=1~cowtan/sfapplet/sfintro.html=Whatisaconvolution?–Toconvolutetwofunctions,thefirstfunctionmustbesuperimposedonthesecondateverypossibleposition,andmultipliedbythevalueofthesecondfunctionatthatpoint.Theconvolutionisthesumofallofthesesuperpositions.函数(x)x0xo(x-xo)dx＝1(x-xo)f(x)dx＝f(xo)＝0,如果x≠xo＝1,如果x＝xo(x-xo)函数阵列(x)xn=-,(x-na)L(x)＝01a2a3a4a5a6a-1a-2a-3a-4a……===r0r0r1r1晶体电子密度函数是晶胞电子密度函数与空间点阵函数的卷积_crystalunitcellnmpnmprrrabcConvolutionTheorem•TheFouriertransformofaconvolutionistheproductoftheFouriertransforms•TheFouriertransformofaproductistheconvolutionoftheFouriertransforms晶体衍射强度晶体衍射强度受很多因素影响：•入射光强度•晶体体积•晶体中包含的晶胞数目•……….这些因数合并为一个常数K表示晶体衍射强度还有一些因数随衍射指标hkl和衍射角（2）不同，对衍射强度有不同的影响。I’=KLPTA|F|2L：洛伦兹因子P：偏极化因子T：温度因子A：吸收因子偏极化因子(PolarizationFactor)P2=(1+cos22)/2P2称为偏极化因子(polarizationfacor,P)洛伦兹因子(LorentzFactor)•Aseachlatticepointonthereciprocallatticeintersectsthediffractometercircle,adiffractionrelatedtotheplanerepresentedwilloccur.•Asanglesincrease,theintersectionapproachesatangenttothecircle;thusathigherangles,moretimeisspentinthediffractingcondition.•ThisincreasedtimewillbeafunctionofthediffractionangleandmaybecorrectedbyinsertingthetermI/(sin2cos)intotheexpressionforcalculatingdiffractionintensities.•ThistermiscalledtheLorentzfactor.Inpractice,thisisusuallycombinedwiththeatomicscatteringpolarizationterm(Thompsonequation)andcalledtheLorentzpolarization(Lp)correction.晶体衍射强度I=I’/PL=K|F|2exp[-2B(sin2/2)若能求出K值和B值，就可以从实验得到的经过PL修正的相对强度值，引出结构因子的振幅|F|。利用Wilson作图法，可求出K和B值。即可求出|F|值，但我们失去了相角信息（晶体学中重要的相角问题）。