上海交通大学：《材料组织结构表征》课程教学资源（课件讲义）X射线衍射6-晶格参数的精确测定

http://www.periodictable.com/Properties/A/LatticeConstants.sp.wt.html 六、晶格参数的精确测定 80 60 40 20 0 20 40 60 80 100 Atomic Number

六、晶格参数的精确测定 http://www.periodictable.com/Properties/A/LatticeConstants.sp.wt.html

六、晶格参数的精确测定 ·问题的提出 ·误差来源 一测角仪、装样、单色器 实验参数设定 一管流、管压、扫描速度、狭缝 一 数据处理 ·方法

六、晶格参数的精确测定 • 问题的提出 • 误差来源 – 测角仪、装样、单色器 • 实验参数设定 – 管流、管压、扫描速度、狭缝 – 数据处理 • 方法

An accuracy of at least 0.06%is required. Experiment data sum of peak 1 and peak 2 peak 1-y' peak 2-y 分峰条件： 峰形Voigt Accelerating Voltage Camera Length Magnification 200kV 10000× 500nm 置信度99% 采集条件： Misfit:0.15~0.35% 0.01/step 4s/step 72 7374 75 76 77 78 20

 ’ 采集条件： 0.01o /step 4s/step 分峰条件： 峰形 Voigt 置信度 99% An accuracy of at least 0.06% is required. Misfit: 0.15~0.35% (220)

In-situ high-T XRD-TisSig 2242) (3251) Intensity(arbitary unit) 0 200 *L.T.Zhang and J.S.Wu,Scripta 400 59 Materialia,38(1998)307 60 600 0.755 61 29 64 800 Temperature Ti Sia 65 1000 66 0.7501 0.525 ● 0.745 0.520 0.740 0.515 ● ● a-axis c-axis 0.735 0.510 0 200 400 600 800 1000 0 200 400 600 800 1000 Temperature(C) Temperature(°c)

*L.T. Zhang and J.S. Wu, Scripta Materialia, 38(1998)307 In-situ high-T XRD-Ti5Si3

Profile E Strongest 3 peaks no.peak 2Theta d I/I1 FWHM no. (deg) (A) (deg) 1 1 28.3699 3.14332 100 0.11470 2 2 47.2380 1.92256 55 0.10980 56.0600 1.63912 36 0.10770 4000- Peak Data List peak 2Theta d I/I1 FWHM no. (deg) (A) (deg) 1 28.3699 3.14332 100 0.11470 23 47.2380 1.92256 55 0.10980 56.0600 1.63912 36 0.10770 69.0791 1.35858 8 0.11400 76.3222 1.24666 14 0.11000 220 6 87.9814 1.10905 17 0.12150 94.9030 1.04557 8 0.12970 2000 891011 106.6626 0.96033 5 0.15280 114.0568 0.91816 10 0.14960 127.5153 0.85879 8 0.17250 136.8696 0.82826 4 310 0.18340 (400) (33) 51 440 (5311) 620 100 120

(111) (220) (311) (400) (331) (422) (511) (440) (531) (620) (533)

Profile h k 2theta d(A) a(A) 1 1 28.3699 3.14332 5.44439 2 0 47.238 1.92256 5.43782 4000- 2000 12343454565 10 56.06 1.63912 5.43635 69.0791 1.35858 5.43432 3 76.3222 1.24666 5.43406 2 2 87.9814 1.10905 5.43321 1 1 94.903 1.04557 5.43294 4 0 106.6626 0.96033 5.43245 323 114.0568 0.91816 5.43191 0 127.5153 0.85879 5.43146 3 136.8696 0.82826 5.43126 60 100 120

h k l 2theta d(A) a(A) 1 1 1 28.3699 3.14332 5.44439 2 2 0 47.238 1.92256 5.43782 3 1 1 56.06 1.63912 5.43635 4 0 0 69.0791 1.35858 5.43432 3 3 1 76.3222 1.24666 5.43406 4 2 2 87.9814 1.10905 5.43321 5 1 1 94.903 1.04557 5.43294 4 4 0 106.6626 0.96033 5.43245 5 3 1 114.0568 0.91816 5.43191 6 2 0 127.5153 0.85879 5.43146 5 3 3 136.8696 0.82826 5.43126

误差来源 λ d 2sine △几 λ△0cos& △d= 2sin0 2sin2 0 △d △入 △0cosθ d λ sinθ

误差来源       2 2sin cos 2sin    d    2sin d       sin  cos     d d

1.0 不 △sin0 0.8- 0 uis 0.6- △0→ 0.4- 0.2 0.0 0 20 40 60 80 0(degrees) △d △2 △0cos0 The fractional error approaches d 几 sin0 zero as 0 approaches 900

     sin  cos     d d The fractional error approaches zero as  approaches 90o

10 λcos0 od o0 2 sin2 0 8 The fractional error approaches 6 zero as 0 approaches 90. 00=0.01° 4- σ0=0.02° 2 o0=0.005° 0 0 10 20 30 40 50 60 70 80 90 Bragg angle,θ(deg)

The fractional error approaches zero as  approaches 90o

Accuracy is critical If we want to know the lattice parameter to within 1x10-5 nm,we must know the peak position to within0.02°at20=160°

Accuracy is critical • If we want to know the lattice parameter to within 1x10-5 nm, we must know the peak position to within 0.02o at 2=160o