现代材料研究方法TEM1

Weiss’s Zone Law
1. Basic law: hu + kv + lw = 0 . 2. Addition rule If (h1k1l1) and (h2k2l2) belong to [uvw], then (h3k3l3) also belongs to [uvw] when: h3 = ±nh1 ± mh2 k3 = ±nk1 ± mk2 l3 = ±nl1 ± ml2 3. Zone axis If (h1k1l1) and (h2k2l2) belong to [uvw], then: [uvw] = (h1k1l1) x (h2k2l2) or u = k1l2 – k2l1 v = l1h2 – l2h1 w = h1k2 – h2k1 4. If a plane (hkl) contains the zone axis [u1v1w1] and [u2v2w2], then: (hkl) = (u1v1w1) x (u2v2w2) or h = v1w2 – v2w1 k = w1u2 – w2u1 l = u1v2 – u2v1
hkl → uvw :
u v 2w c 2 ( ) 2h k h 2k 3l a
2.8. Indexing of simple SAD patterns from hex crystals
2.8.1 Weiss’s zone law 2.8.2 Application of Weiss’s zone law to hex system 2.8.3 Three axis and four axis system for hex crystals 2.8.4 The indices of a plane and its normal in hex crystals
Cos 1 3 a2 h1h2 ( h1k 2 h2 k1 ) k1k 2 ll 2 1 2 2 4c 3 a2 2 2 3 a2 2 ( h12 h1k1 k12 l )( h2 h2 k 2 l ) 2 1 2 2 4c 4c
The indices of a plane and its normal in hex crystals
EM1 Electron Diffraction Patterns
(1) Photograph A is from one grain of a thin foil of a-iron. Choose one spot as the origin and measure the distance of a number of adjacent spots from it. It is always helpful to make a reasonable sketch of the pattern and to label the spots. From the ratio of the distances between the origin and the measured spots, and the known possibilities for values of , assign a consistent set of indices to all the spots and hence determine the indices of the direction of the electron beam. Given that the unit cell dimension of a-iron is 2.86 Å, what is the "camera constant" for the photograph? (2) Index the pattern B given that it is from aluminum, a= 4.04 Å and that the camera constant is approximately 4.4 cm. Å (3) The diffraction pattern C is from a-iron containing precipitates of CrN (fcc, a= 4.15 Å which have a definite orientation relationship with the matrix. The precipitates occur as thin plates on the three sets of (100)a planes so there are three precipitate patterns present on the photograph. The sketch D shows only one precipitate pattern, plus the matrix pattern. Note the symmetry of the matrix pattern and index it by inspection. Index the precipitate pattern and determine the orientation relationship between precipitate and matrix. Account for the observed morphology of the precipitate particles.
2.5. 衍射花样的形状效应 Shape effect of diffraction patterns
Leabharlann Baidu
2.6.取向关系（Orientation relationship）
2.7. 入射束方向的精确确定 Accurate determination of beam direction
现代材料研究方法
引言:
1. 现代材料科学 2. 材料科学发展趋势 3. 电子显微镜及微区分析在材料科学研究中的作用
材料科学概念
加工 性能 性能
成本（性能、价格比） 成本
加工 成份 成份 组织 性能 加工 成份 组织 性能
组织
成份 组织
环境
材料科学发展趋势
• 传统材料(Traditional materials): 提高性能/价格比 • 先进材料 (Advanced materials): 用于各种极端条件 • 功能材料（Functional materials) • 低维材料（ Low dimension materials） • 纳米技术和纳米材料（Nano technology and nano materials） • 生物医学材料（Biomaterials） • 环境材料（Environmental materials） • …………….
2.1. 电子衍射（Electron diffraction）
2.2. 选区电子衍射（Selected area electron diffraction (SAD)）
2.3. 相机常数（Camera constant）
Ll 叫作相机常数, 且 dhkl = Ll /R’
2.4 简单SAD花样的标定（Indexing of simple SAD patterns）
2.4.1尝试校核法（ Trier and error: ） 2.4.2 已知相机常数法（Known camera constant） 2.4.3 标准衍射谱法（Standard diffraction patterns） 2.4.4 计算机标定法（Computer simulation）
R1 2 N1 h12 k12 l12 ( ) 2 2 2 R2 N 2 h2 k 2 l2
1. 引言（Introduction）
1.1. 阿贝成象理论（Abby’s theory of image formation） 1.2. 电子显微镜（Electron microscope） 1.3. 衬度的起源（Origin of image contrast） 1.4. 电镜图像举例（Examples of electron microscopy photographs）
本课程的内容:
Part I 透射电子显微学及其在材料科学研究中的应用 Part II 高分辩电子显微学及其在材料科学研究中的应用 Part III 分析电子显微学及其在材料科学研究中的应用
Part I 透射电镜及其在材料科学研究中应用
1. 引言 2. 电子衍射（Electron diffraction） 3. 衍衬理论（Theory of diffraction contrast） 4. 完整晶体的特征图像（Characteristic images from perfect crystals） 5. 位错和层错的衬度（Contrast from dislocations and stacking faults） 6. 第二相粒子的衬度（Contrast from second phase particles） 参考资料（References） :
2.1. 电子衍射（Electron diffraction） 2.2. 选区电子衍射（Selected area electron diffraction (SAD)） 2.3. 相机常数（Camera constant） 2.4. 简单电子衍射花样的标定（Indexing of simple SAD patterns） 2.5. 衍射花样的形状效应（Shape effect of diffraction patterns） 2.6. 取向关系（Orientation relationship) 2.7. 入射束方向的精确确定 （Accurate determination of beam direction） 2.8. 复杂衍射花样（Complicated SAD patterns） 2.9 偏移参数（Deviation parameter sg）
h2k2l2
R2 a 000 R1 h1k1l1 R3
h3k3l3
cosa
h1h2 k1k2 l1l2
2 2 2 h12 k12 l12 h2 k2 l2
B = R1 x R2
fcc : N=3, 4, 8, 11, 12, 16, 19,……. bcc : N= 2, 4, 6, 8, 10, …….
阿贝成象理论（Abby’s Theory of Image Formation）
Optical Microscope
Electron Microscope
非晶样品（Amorphous Specimen）
B
A
晶态样品（Crystalline Specimen）
2.电子衍射（Electron Diffraction）
1. Electron Microscopy of Thin Crystals, M.A.Hirsh et al., 1977 2. Transmission Electron Microscopy of Materials, G.Thomas, 1979 3. Practical Electron Microscopy in Materials Science, J.W. Edington,1974-77 4. Defect Analysis in Transmission Electron Microscopy, R.E.Smallman, 1980 5. 电子衍射图在晶体学中的应用, 郭可信等 6. 金属电子显微分析, 上海交大
Three axis to four axis system
Planes:
(hkil) = (HKL) h+k+i+l=0 h=H k=K l=L Directions: [uvtw] = [UVW]
u 2U V 3 v 2V U 3
w=W
U=u–t V=v–t W=w Angles: