X射线衍射仪的原理及其在高分子科学中的应用张吉东

1、X射线衍射仪的原理及其在高分子科学中的应用X-ray diffractometer: Principle and Application in Polymer Science张吉东Tel: 2897; 2012.04X射线衍射的原理X射线衍射仪及操作X射线衍射表征高分子Crystal: solid with repetitive internal structure; a solid containing an internal pattern of atoms, molecules, or ions that is regular, repeated, and geometrically a

2、rrangedX射线衍射原理 = OA PB = OP s OP s0 = OP (s s0) = ma (s s0)Laue equationa (cos - cos0) = Hb (cos - cos 0) = Kc (cos cos 0) = L = AB + BC = dsin + dsin = 2dsinBragg equation: 2dsin = nX射线衍射原理Bragg equation: 2dsin = nX射线衍射原理X射线衍射测试方法：照相法平面底片法平面底片法 圆筒底片法圆筒底片法 X射线衍射测试方法：照相法德拜德拜谢乐法谢乐法 X射线衍射测试方法：照相法X射线衍射测

3、试方法：衍射仪法衍射仪：X射线源X射线也是一种电磁波波长范围 0.01100X-ray applicationuMedical graphuCrystalline structureuThickness, density and roughnessuother产生X射线的方式主要有以下四种：X射线管射线管、激光等离子体、同步辐射同步辐射和X射线激光。 Efficiency 0.2%实验室用X射线源封闭X射线管Sealed Tube40KV 40mA辉度109旋转阳极靶Rotating Anode50KV 300mA辉度1010衍射仪：X射线源实验室用X射线源CuK=1.5418 ; CuK=1

4、.3922 MoK=0.7107 ; CrK=2.2909衍射仪：X射线源实验室用X射线源Soller slitMultilayer mirrorMultilayer mirror衍射仪：X射线源同步辐射的X射线源衍射仪：X射线源同步辐射的X射线源衍射仪：X射线源上海同步辐射光源北京同步辐射光源/正负电子对撞机合肥同步辐射光源新竹同步辐射光源衍射仪：X射线源ESRF，欧洲/法国Spring8，日本APS，美国DESY，德国SPEAR，美国Dimond，英国衍射仪：X射线源X射线激光 正因为X射线的应用越来越广泛，科学家着重研究增加X射线的强度。世界上第一个红宝石激光1960年问世以来，在X射线

5、波段实现激光辐射就一直是激光研究的重要目标。射线激光除了具有普通激光方向性强、发散度小的特点外，其单光子能量比传统的光学激光高上千倍，具有极强的穿透力。 X射线自由电子激光 自由电子激光是一种以相对论优质电子束为工作媒介、在周期磁场中以受激辐射方式放大短波电磁辐射的强相干光源（其“周期磁场”由波荡器产生），具有波长范围大、波长易调节、亮度高、相干性好、脉冲可超短等突出优点，尤其是高增益短波长自由电子激光，普遍被看好是下一代光源的代表，具有巨大的发展潜力和重大的应用前景。衍射仪：X射线源衍射仪：测角仪立式测角仪卧式测角仪2两圆测角仪SourceStageDetectorP P P P P P 衍

6、射仪：测角仪多圆测角仪衍射仪：测角仪多圆测角仪衍射仪：测角仪其他附件薄膜台纤维架衍射仪：探测器点探测器闪烁计数器正比计数器半导体探测器衍射仪：探测器一维探测器Vantec1500 channelLynxeye192 channelPIXcel Dtex-Ultra衍射仪：探测器二维探测器IP板的新生衍射仪：探测器二维探测器MarAPEX II CCDHiStar二维多丝探测器衍射仪：整机高分子材料一般很难培养出单晶四圆单晶衍射仪日本理学DMax2500大功率X射线衍射仪德国Bruker D8 Discover薄膜X射线衍射仪衍射仪：整机日本理学SmartLab微区X射线衍射仪衍射仪：整机衍射仪

7、：整机衍射仪：整机Locked coupledLow angle: X-ray ReflectivityWide angle: Wide angle X-ray DiffractionUnlocked coupledUncoupledGrazing-incident X-ray ReflectivityRocking curve衍射仪：操作AlignmentDetector scan: =0, Z=-5;scan 2detectorZ scan: =0, 2 =0; scan ZZRocking curving: 2 =0,Zi;scan i 2 =0.4,Zi;scan Chi: =0.2,

8、 2 =0.4; scan ChiChiZ scan: =0, 2 =0; scan ZZRocking curving: 2 =0.4,Zi;scan i*Z sample stage height; ,Chi sample stage angle /Rx,RyFor powder, only Z scan at / 2 of diffraction peak is needed衍射仪：操作MeasurementXRR: Cu absorber change twice in locked coupled modeWXRD: without Cu absorber in locked cou

9、pled modeGIXRD: without Cu absorber in detector scan modeAnalysisXRR:thickness, roughness, density, concentration distributionWXRD: phase, orientation, crystallization ratioGIXRD: phase, orientation, layer sequence衍射仪：操作衍射仪：操作衍射仪：操作EVA: Diffraction analysis衍射仪：操作衍射仪：操作 求解晶体结构 确定晶型 计算结晶度 计算微晶尺寸 计算取向度

10、 计算应力i-PPPEX射线衍射表征高分子材料)2cos2cos2coscoscoscos21 (121hkld)coscos(cos222sin222sin222sin2abhkclbkah)coscos(cos2)coscos(cos2achlbcklTetragonalOrthorhombica b c, = = = 90oTriclinica b c, Hexagonala = b c, = = 90o , =120oMonoclinica b c, = = 90oTrigonalCubica = b =c, = = = 90oa = b c, = = 90o , =120oa = b

11、 c, = = 90o a = b , = = = 90o X射线衍射表征高分子材料位置晶型不同晶型聚丙烯X射线衍射表征高分子材料-PP-PP-PP()2 ()强度hkl()2 ()强度hkl()2 ()强度hkl6.2614.16最强1106.3713.90很强1116.2414.18弱2105.1917.08很强0405.2916.76很强0085.5116.08最强3004.7718.60很强1304.4220.20很强1174.58219.37弱3104.1921.20强1114.1921.70强2024.2021.15中强3014.0421.94很强310414.0521.90强02

12、64.1321.53弱4003.4825.58弱0603.8523.10弱221晶型,单斜晶系:a0.665nm，b2.096nm，c0.650nm，99.3o晶型,六方晶系:a1.274nm，b1.274nm，c0.635nm晶型,正交晶系:a0.854nm，b0.993nm，c4.241nm位置晶型axccx, cIKIIWIc及Ia分别为在适当角度范围内的晶相及非晶相散射积分强度；Kx系校正常数; %100)()()()()()(,ijjjhklihkliihklihkliixckICICICWi,j分别为计算结晶衍射峰数目和非晶衍射峰数目；Ci,hkl()，Ii,hkl()分别是hkl

13、晶面校正因子及衍射峰积分强度； Cj()，Ij()分别系非晶峰校正因子和散射峰积分强度. %10010. 199. 450. 357. 199. 450. 357. 1201111210200110010201111210200110010,axcIIIIIIIIIWPE的WAXD曲线分解 X射线衍射表征高分子材料强度结晶度X射线衍射表征高分子材料峰宽微晶尺寸、微应力Schrerrer公式L(hkl)=k/cos1) 近似函数法 2) Warren-Averbach Fourier 分析法3) Fourier 单线分析法 4) Hosemann 次晶模型法5) 方差函数法6) 四次矩法Lhkl

14、 是垂直于 (hkl) 晶面的平均微晶尺寸 (nm)； 为入射 X 射线的波长 (nm)； 为 Bragg 角； 为衍射线宽(用弧度表示)； k 为 Scherrer 形状因子. 10203040506005000100001500020000I(cps)2(100)(110)(200)(120)(014)(201) X射线衍射表征高分子材料峰分布取向 Stein 正交晶系取向模型 Wilchinsky 非正交晶系取向模型 照相法拉伸 PE X 射线衍射强度图 X射线衍射表征高分子材料51015202530As-spin-coatingAnnealedSi/SiO2/OTS/P3HTInten

15、sity2 /oSi/CuPcSi/SiO2/OTS/P3HT厚度掠入射X射线衍射优点可避免或消除基底影响，同时加大照射面积 面内面外方向均可扫描，可以分析三维微结构可以控制入射深度，进行层序分析掠入射X射线衍射X射线衍射表征高分子材料NiiAfANerNiiAfiZANerin1221221, n=1- NA Avogadro constant re electron diameter 2.814e-15m DensityZi electron numberAi atom weightf dispersion factorf” absorption factor X射线衍射表征高分子材料掠入

16、射X射线衍射Total reflection densitynsample / nair = cossample / cosair air=0, nair =1,nsample= 1 cosc = 1 ; cosc = 1 c2/2c = (2 )1/2; c 1/2Total reflectionAt the interface, luminous ray at which it is wholly reflected, and no portion of it transmitted.Critical angle That angle of incidence of luminous ra

17、y in total reflectionPolymer 0.15o0.18oSiO2 0.21o Si 0.22oX射线衍射表征高分子材料掠入射X射线衍射L = L0 / sin掠入射X射线衍射0.2mm0.5o22.9mm0.2mm20o0.6mmSi/SiO2/6P/ZnPc21)22(242)22(2ciciX射线衍射表征高分子材料CH2CH2On10203040506005000100001500020000I(cps)2(100)(110)(200)(120)(014)(201) monoclinica= 8.05 b=13.04 c=19.48 =125.4o1020304002

18、00040006000LC Intensity2GID(014)(120)(200)(201)(110)X射线衍射表征高分子材料掠入射X射线衍射102030401021031041234102103104105106107108I(cps)2(o)110120102014 a PEOPS1020304010100100024102103104105106107108I(cps)2(o) eX射线衍射表征高分子材料掠入射X射线衍射51015202530Solvent treated / XRDSolvent treated / GIXRDIntensity /a.u.2heta oAs spin

19、-coating / GIXRD350400450 400450500 As spin-coating Solvent treatedAbsorbance /a.u.Wavelength /nmPL intensity /a.u.UV and PL spectra of PFO film before and after solvent vapor treatmentNormal XRD and GIXRD of PFO film before and after solvent vapor treatmentX射线衍射表征高分子材料掠入射X射线衍射51015202530Intensity2P

20、owder51015202530 amorphous alpha1 alpha betaIntensity 2Thin film通过加热、溶剂熏蒸、熔融结晶发现薄膜中存在非晶相以及结晶相、和向列相（N）X射线衍射表征高分子材料掠入射X射线衍射8121620Aging 6 daysAging 3 daysFreshI /a.u.2 Theta / o(008)Out of planein plane400425450475500PL IntensityWavelength 0Day3Day6Day4004254504755006Day3Day0DayPL IntensityWavelength

21、5101520Intensity q / nm-1Fresh3days6days溶液凝胶化对PFO薄膜微结构的影响X射线衍射表征高分子材料掠入射X射线衍射X射线衍射表征高分子材料掠入射X射线衍射BP2T有机小分子半导体不同厚度薄膜的面内掠入射X射线衍射图BP2T有机小分子半导体分子式与晶体结构单层与五层BP2T薄膜的电子衍射花样JPhysChemB2010(114)4821X射线衍射表征高分子材料掠入射X射线衍射X射线衍射表征高分子材料掠入射X射线衍射110nmPFO薄膜的面外掠入射X射线衍射图X射线衍射表征高分子材料掠入射X射线衍射#5#6X射线衍射表征高分子材料掠入射X射线衍射BPPh和B

22、PTT两种薄膜的二维掠入射X射线衍射图BPPh和BPTT两种薄膜的面内掠入射X射线衍射图BPPh和BPTT两种薄膜的选区电子衍射花样ssX射线衍射表征高分子材料掠入射X射线衍射10101520202530303540404550502Theta /oI0.08o1.0oX射线衍射表征高分子材料掠入射X射线衍射法线1法线212PEAg3X射线法线3角 度穿透深度/m角 度穿透深度/m0.106.340.4037.670.128.980.5047.390.1411.330.6057.070.1512.450.7066.720.1613.550.8076.350.1815.690.9085.980.

23、2017.771.0095.590.2522.862.00191.590.3027.853.00287.500.3532.774.00383.39X射线衍射表征高分子材料掠入射X射线衍射102030405002000400060008000100001200014000160002009-12-15 21:20:14Phi 90stretch directionPhi 02Theta /o透射Total reflection densitynsample / nair = cossample / cosair air=0, nair =1,nsample= 1 cosc = 1 ; cosc

24、= 1 c2/2c = (2 )1/2; c 1/2Total reflectionAt the interface, luminous ray at which it is wholly reflected, and no portion of it transmitted.Critical angle That angle of incidence of luminous ray in total reflectionReflectivityPolymer 0.15o0.18oSiO2 0.21o Si 0.22oX射线衍射表征高分子材料ReflectivityInterferenceTh

25、e mutual influence, under certain conditions, of two streams of light, or series of pulsations of sound, or, generally, two waves or vibrations of any kind, producing certain characteristic phenomena, as colored fringes, dark bands, or darkness, in the case of light, silence or increased intensity i

26、n sounds; Interference thicknessm2 = m2 2 / 4d2 + c2d = / 2 (m+1 - m )Kiessig oscillationX射线衍射表征高分子材料EVA* Our system d = 8.8 / 2 (nm)d = / 2 (m+1 - m )ReflectivityX射线衍射表征高分子材料Simulation & Fitting Software1.Leptos SimplexSimulated AnnealingLevenberg-MarquardtGenetic algorithm2.REFSIMSimplexSimulated AnnealingMonte CarloThreshold AcceptanceReflectivityX射线衍射表征高分子材料ReflectivityX射线衍射表征高分子材料ReflectivityMultilayerX射线衍射表征高分子材料ReflectivityRoughnessSiO2/AuActualR 0.3nm/1.2nmR 0.0nm/0.0nmX射线衍射表征高分子材料B.Lehr, M.Seufert, G.Wenz, G.Decher, Fabrication of poly(p