Download - Chap4_Kinematic and Dynamic Scattering
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chapter 4Kinematic and Dynamic Theory
(Chapter 11, 13,18, 24)
(Chapter 11, 13,18)
(Chapter 26)
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4.1 運動學強度(Kinema,cal Intensity)• 回顧:薄膜的電子繞射並不⼀一定要100%滿足Bragg’s繞射條件• Bragg’s繞射條件 2dsinθ = λ k’-‐k0 = g
• 繞射光的強度(結構因子的振幅) 與倒晶格點到Ewald球的距離 有關(s)• 另s為激發誤差(devia,on or excita,on error) (relaxed Bragg’s condi,on)
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運動學理論在以下兩個條件下可被接受為第⼀一近似
(1)當樣品很薄時:沒有足夠的“繞射中心”去建 立足夠強的繞射光(2)當晶體遠離真正的繞射中心時:弱光
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single atom
Io Isc∝ |f(θ)|2
Unit cell
Io∝ |F(θ)|2Isc
Recall
Thin sample
Io
∝ |F(θ)|2Isc
t
dark field
bright field
dark field
bright field dark
field
bright field
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single atom
Io Isc∝ |f(θ)|2
Unit cell
Io∝ |F(θ)|2Isc
Recall
Thin sample
Io
∝ |F(θ)|2Isc
t
dark field
bright field
dark field
bright field dark
field
bright field
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single atom
Io Isc∝ |f(θ)|2
Unit cell
Io∝ |F(θ)|2Isc
Recall
Thin sample
Io
∝ |F(θ)|2Isc
t
Isc
dark field
bright field
dark field
bright field dark
field
bright field
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single atom
Io Isc∝ |f(θ)|2
Unit cell
Io∝ |F(θ)|2Isc
Recall
Thin sample
Io
∝ |F(θ)|2Isc
t
Isc
Ω為晶胞體積繞射強度以單位晶胞體積為標準
dark field
bright field
dark field
bright field dark
field
bright field
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定義:
運動學強度•光只被散射一次•ISC<< I0 = 1 (遠離Bragg’s條件)
• ξxg = ~µm
• ξg我們稱之為消光距離(extinction distance)• 消光距離的物理意義就是當試片的厚度大於ξg時,散射光g 的強度大於入射光強度(入射光的能量完全轉移至散射光方向)• 我們因此必須考慮到由散射光束所引起之第二次散射。我們 稱之為動力學效應(dynamical effect)。
ξg
IscI0 (二次波源)
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(Chapter 18)
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(Chapter 18)
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Si[130]
Double Diffraction (Chapter 18)
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4.2 Kinematic Contrast- mass/ thickness contrast- Bragg (orientation) contrast
Bright Field Dark Field
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Io=1-Isc
4.2.1 Thickness Fringe
Bright Field Dark Field
Wedge Shape
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IscIo=1-Isc
4.2.1 Thickness Fringe
Bright Field Dark Field
Wedge Shape
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(II) Thickness Fringes
• 明場與暗場像是 運動學的範圍才 可能是互補
•在運動學的範圍內有吸 收的因素,明場與暗場 之強度沒直接的關係
Dark FieldBright Field
Wedge Shape
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an etch pit in a Ge sample which is the usual inverted pyramid with {111} planes
(III) Thickness Fringes
GaAsGaAs tt
傾斜晶界
化學浸蝕破洞
MgO
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4.2.2 Mass Contrast
CuMgO
CuMgO
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4.2.3 Bend Contours (Bragg contrast)(實空間結晶訊息)
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4.3
Strain Contrast(defects: dislocation, interface, stacking fault)
電子繞射動力學 (Dynamic Diffraction Theory)
•當
Ψg可以當成二次波源,這時運動學不適用,必須考慮‘’動力學“
•對運動學而言,穿透光和繞射光不互相干擾
動力學而言,穿透光和繞射光互相修正(影響)
•考慮雙光束條件,只有一個g很強被激發,其他的繞射光
S>>0或S<<0
(Chapter 13)
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4.3.1 Howie- Whelan Equation
其解, 動力學強度
運動學強度
Seff=[(s2+1)/ξ2]1/2
有效的激發誤差 (描述電子與
樣品作用之強弱) 則
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•當S=0時,Seff =ξg-1 I0 =1-Ig
•當|S|很大時,S~Seff (動力學退化與運動學相重合):弱光束
Seff=[(s2+1)/ξ2]1/2
有效的激發誤差 (描述電子與樣品作用之強弱) 則
有晶格扭曲時(或位移),Howie-Whelan Eqn.之修正連續R 固定R
因為缺陷因素引起相位之變化
˙
˙
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Edge Dislocation (邊刃差排)
R
b
rΦ
4.3.2 Line Defects
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• 若g · R=0 則雖有缺陷,但不引起對比
• g · R是因為缺陷之應變場,使晶格扭曲,變形或位移,所以 在TEM影像我們看到的是缺陷的應變場
•若R(r)延續很遠(長程應變)則缺陷之影像是很寬的;相反的,若R (r) 是非常局部化則缺陷之對比亦侷限在很小區域
有晶格扭曲時(或位移),Howie-Whelan Eqn.之修正連續R 固定R
因為缺陷因素引起相位之變化
˙
˙
(Chapter 26)
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•因為局部應變場的變化,使得每一個column的繞射條件皆不同( 不同)
•因而產生對比之分佈
•事實上,我們看到的是入射電子與應變場之作用結
果(g · R 對比)
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• 繞射光偵測不到差排應變場對晶格的扭曲
所以dislocation沒有對比
g · b( g · R= 0)是用來測定 dislocation Burgers Vector 的準則
No contrast
g
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partial dislocations
At the bottom surface: the contrast in BF and DF are complementary
At the top surface: the contrast in BF and DF are same
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APB (or IDB) of GaAs
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Dislocation in Σ13 Grain Boundary of Zn
g1
g2
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