清华大学-蛋白质晶体学课件-6.pdf

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1、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.OnecycleperperiodA·cos(2k

2、x+)11k=11A·cos(2kx+)kkk=1k=2.TwocyclesperperiodA·cos(2kx+)22k=22A·cos(2kx+)kkk=1k=3.ThreecyclesperperiodA·cos(2kx+)33k=33A·cos(2kx+)kkk=1FourierSynthesis.NCyclesA·cos(2kx+)33k=3NA·cos(2kx+)kkk=1http://www.ysbl.york.ac.uk/~cowtan/sfapplet/sfintro.htmlWhatisacon

3、volution?–Toconvolutetwofunctions,thefirstfunctionmustbesuperimposedonthesecondateverypossibleposition,andmultipliedbythevalueofthesecondfunctionatthatpoint.Theconvolutionisthesumofallofthesesuperpositions.=(x)＝0,如果x≠xo函数(x-xo)＝1,如果x＝xo(x-xo)dx＝10xox(x-xo)f(x)dx＝f(xo)(x

4、)函数阵列L(x)＝(x-na)n=-,x…-4a-3a-2a-1a01a2a3a4a5a6a…r1r1rr00===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crystalrrraunitcell_bcnmpnmpConvolutionTheorem•TheFouriertransformofaconvolutionistheproductoftheFouriertransforms•TheFouriertransformofaproductistheconvolutionoftheFou

5、riertransforms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

6、F

7、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)/2P称为偏极化因子(polarizationfacor,P)2洛伦兹因子(LorentzFactor)•Aseachlatticepointontherecipro

8、callatticeintersectsthediffractometercircle,adiffractionrelatedtotheplanerepresentedwilloccur.•Asanglesincrease,theintersectionapproachesatangenttothecircle;thusathigherangles,moretimeisspentinthediffractingcondition.•Thisincreasedtimewillbeafunctionofthediffractionangleandmaybe

9、correctedbyinsertingthetermI/(sin2cos)intotheexpressionforcalculatingdiffractionintensities.•ThistermiscalledtheLorentzfactor.Inpractice,thisisusuallycombinedwiththeatomicscatteringpolarizationterm(Thompsonequation)andcalledtheLorentzpolarization(Lp)correction.晶体衍射强度I=I’/PL=K

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11、F

12、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