第四章电子衍射2_11-9-30讲义
电子衍射
（ ）表示平面，*表示倒易， 0表示零层倒易面。
这个倒易平面的法线即正空 间晶带轴[uvw]的方向，倒易平 面上各个倒易点分别代表着正空 间的相应晶面。
0
4. 晶带轴的求法
若已知零层倒易面上任意二个倒易矢量的坐标， 即可求出晶带轴指数.由
得
u=k1l2-k2l1
v=l1h2-l2h1
简单易记法 h1 k1 l1 h1 k1 l1
Hot- and Cold-Stage TEM
20oC a 220oC b 25oC
c
AFE-1 AFE FE
d -100oC
a and b: PbZrO3 single crystal C and d: Pb(ZrSnTi)O3 ceramic
AFE-2
七、多晶电子衍射成像原理与衍射花样特征
图8-2 多晶电子衍射成像原理
金的原子力显微镜照片
倒易点阵
正点阵：晶体点阵
倒易点阵：与正点阵存在倒易关系
a*•b=a* • c=b* • a=b* • c=c* • a=c* • b=0
a* • a=b* • b=c* • c=1
写成标量形式
a*=1/a×cosφ b*=1/b×cosψ c*=1/c×cosω
ω
与正点阵的关系
反射式高能电子衍射分析(RHEED):以高能
电子照射较厚样品分析其表面结构，电子 束以掠射方式(与样品表面的夹角小于5o) 照射样品，使衍射发生在样品浅表层。
RHEED用荧光屏作结果显示，在超高真空
环境下工作。
低能电子衍射(LEED)：电子束能量为10~1000eV (一般为10~500) 。由于电子能量低，衍射结果 只能显示样品表面1~5个电子层的结构信息，因 此是分析晶体表面结构的重要方法，广泛用于 表面吸附、腐蚀、催化、外延生长、表面处理 等材料表面科学与工程领域。 低能电子衍射仪器为低能电子衍射仪，也是在 超高真空环境下工作。
《电子衍射原理》课件
透射电子显微镜技术
透射电子显微镜技术是一种利用透射 电镜观察物质内部微细结构的方法， 具有高分辨率和高放大倍数的特点。 随着科技的不断进步，透射电子显微 镜技术的应用范围越来越广泛，在材 料科学、生物学、医学等领域得到广 泛应用。
VS
例如，在材料科学领域，透射电子显 微镜技术可用于研究材料的晶体结构 和相变行为，为新材料的开发和优化 提供有力支持。在生物学领域，透射 电子显微镜技术可用于研究细胞器和 生物大分子的结构和功能，为生命科 学和医学研究提供新的视角。
电子显微镜的放大倍数较高，能够观察到非常细微的结构细节，是研究物质结构和 形貌的重要工具之一。
电子源
电子源是电子显微镜中的核心部件之一，它能够产生用于观察和成像的 电子束。
电子源通常由加热阴极、栅极和加速电极等部分组成，通过加热阴极使 得电子逸出并经过栅极和加速电极的调制和加速，形成用于成像的电子
电子衍射可以揭示细胞内部的超微 结构，有助于理解细胞的生理和病 理过程。
在表面科学中的应用
表面晶体结构
电子衍射可以用于研究固体表面 的晶体结构和化学组成，对表面 改性和催化等应用具有指导意义
。
表面应力分析
通过电子衍射可以分析表面应力 状态，有助于理解表面行为的物
理机制。
表面吸附和反应
电子衍射可以研究表面吸附分子 的结构和反应活性，对表面化学 和工业催化等领域有重要意义。
05
电子衍射的发展前景
高能电子衍射技术
高能电子衍射技术是一种利用高能电子束进行物质结构分析的方法，具有高分辨 率和高灵敏度的特点。随着科技的不断进步，高能电子衍射技术的应用范围越来 越广泛，在材料科学、生物学、医学等领域发挥着重要作用。
例如，在材料科学领域，高能电子衍射技术可用于研究材料的微观结构和晶体取 向，为新材料的开发和优化提供有力支持。在生物学领域，高能电子衍射技术可 用于研究生物大分子的结构和功能，为药物设计和疾病治疗提供新的思路。
电子衍射讲义
Aims previous | next On completion of this TLP you should:∙Understand why the spots on an electron diffraction pattern appear where they do.∙Know how to index a diffraction pattern from a sample with a known lattice.Introduction:Electrons can act as waves as well as particles; this is a consequence of quantum mechanics. A series of electrons hitting an object is exactly equivalent to a beam of electron waves hitting the object and it produces a diffraction pattern in the same way as a beam of X-rays does.The two important differences between electron and X-ray diffraction are that (1) electrons have a much smaller wavelength than X-rays, and (2) the sample is very thin in the direction of the electron beam (of the order of 100 nm or less) - it has to be thin so that enough electrons can get through to form a diffraction pattern without being absorbed. These factors conspire to have a fortunate effect on the Ewald sphere construction (see The Ewald sphere in the X-ray Diffraction TLP) and diffraction pattern:1. The thin sample makes the reciprocal lattice points longer in thereciprocal direction corresponding to the real-space dimension in which the sample is thin:It should be noted that there is not necessarily always a particular plane oriented like this. However, it is usual for identification of crystallinephases in a sample to orient the sample so that the electron beam isparallel to a low index lattice direction, as this makes the electrondiffraction pattern easier to interpret.2. The small electron wavelength makes the radius of the Ewald spherevery large (recall its radius is 1/λ). The small electron wavelength alsomakes the diffraction angles θ small (1-2°); this can be seen bysubstituting a wavelength of 2.51 x 10-12 m into the Bragg equation (see The Bragg law in the X-ray Diffraction TLP).These make the Ewald sphere diagram look like this so that whole layers of the reciprocal lattice end up projected onto the film or screen:Note that the large (strong) spot in the middle is the straight-through beam (the beam which has passed through the sample without diffracting). This always has the index 000.Caution 1: systematic (kinetic) absences appear in electron diffraction patterns just as in X-ray diffraction patterns, for the same reason: the various features of the lattice or motif diffract electrons in the same direction but the phase factors from the various features cancel, leaving an absence.Caution 2: sometimes where there should be a systematic absence, the spot appears to be still there. This is because of the strong interaction between electrons and atoms: there is a small but significant probability that an electron will be diffracted twice, from two planes one after another - i.e. in two different reciprocal lattice directions one after another. These two directions can add up so that the twice-diffracted electron may arrive at a position in reciprocal space where there is a systematic absence. As an example, the diagram below is a schematic of the [011] electron diffraction pattern of silicon: the 200 type reflections are systematically absent. The intensity at the 200 reflections is caused by double diffraction (arising from the addition of the two reciprocal lattice vectors shown). Thus, in words, intensity can occur in the 200 reflectionfrom, firstly, diffraction from the 11planes, followed by, secondly, difraction by the 1 1 planes as the electron wave passes throught the specimen.Mathematics relating the real space to the electron diffraction patternThe distance, r hkl , on the pattern between the spot hkl and the spot 000 is related to the interplanar spacing between the hkl planes of atoms, d hkl , bythe following equation:(Derivation )where L is the distance between the sample and the film/screen.We can therefore say that the diffraction pattern is a projection of thereciprocal lattice with projection factor L , because reciprocal lattice vectors have length 1/d hkl .Relation 2Since the diffraction pattern is a projection of the reciprocal lattice, the angle between the lines joining spots h 1k 1l 1 and h 2k 2l 2 to spot 000 is the same as the angle between the reciprocal lattice vectors [h 1k 1l 1]* and [h 2k 2l 2]*. This is also equal to the angle between the (h 1k 1l 1) and (h 2k 2l 2) planes, orequivalently the angle between the normals to the (h 1k 1l 1) and (h 2k 2l 2)planes. This angle is θin the diagram below.Using these two relations between the diffraction pattern and the reciprocal lattice, we are now able to index the electron diffraction pattern from a specimen of a known crystal structure.The two pages linked to here refer only to indexing the central region of the diffraction pattern - the rest will be dealt with later.back Indexing with the orientation of the electron beamknownFrom the Ewald sphere diagram, we know that the zero order Laue zone (ZOLZ) contains reflections hkl where hu + kv + lw= 0 (the Weiss zone law). This ZOLZ can be identified by finding two reciprocal lattice vectors in theZOLZ. Suppose these two reciprocal lattice vectors are h1a* + k1b* + l1c* and h2a* + k2b* + l2c*. Then we knowh1u + k1v + l1w= 0andh2u + k2v + l2w= 0and that the angle between these reciprocal lattice vectors is the angle between the h1k1l1 and h2k2l2 planes.Other reflections in the electron diffraction pattern can then be deduced from simple vector addition, with the proviso that the indices of the reciprocal lattice vectors are integers and that they are not forbidden by the lattice. The pattern can then be built up manually or by computer.Example of indexing with a known electron beam orientationbackSuppose the material under examination is copper, and suppose the electron beam direction is [211]. Copper has a cubic close packed structure with a lattice parameter, a, of 0.361 nm. Allowed reflections must have h,k,l either all even or all odd. Thus the planes with the highest interplanar spacings (and hence those that give rise to reflections with the smallest r hkl values) are {111}, {200}, {220}, {311}, {222}, etc.Looking at the {111} planes, it is apparent that the Weiss zone law is obeyedfor (11) when [uvw] =[211]. Hence 11 is a possible reciprocal latticevector.No {200} plane will obey the Weiss zone law for [uvw] = [211], but of the{220} planes it is apparent that (02) will. Hence 02is a second possible reciprocal lattice vector.The angle between the 11 and 02reciprocal lattice vectors is 90° - the dot product of these two reciprocal lattice vectors is zero. The ratio of thelengths of these two reciprocal lattice vectors is . These are the two shortest reciprocal lattice vectors in the [211] electron diffraction pattern. Thus the pattern looks like:back Indexing with the orientation of the electron beamunknownIf we do not know the beam orientation, it is rather more difficult to find which reciprocal plane is the one projected down onto the film.One approach is to consult tables of angles and distance ratios for the low index reflections for the structure of the crystal we are imaging. Again, we will use copper as an example.Table of anglesThe angles in this table are the angles between the reciprocal lattice vectors given at the sides of the table in the appropriate row and column. Such aTable of distance ratiosThe dimensionless numbers in the central portion are the ratios of the 1/d hklexcluded. Thus for copper, which has an F lattice, the reflections are those with h ,k ,l all even or all odd.Now we pick two spots on the diffraction pattern and measure the angle between them and the ratio of their distances from the 000 spot - and see if they correspond to any of the values in the tables.View an exampleOnce we know for sure what two of the non-collinear dots are, we can index the rest of the pattern by vector addition.Example of indexing with an unknown electron beamorientationbackIf were 72.5° and we were to measure the ratio x/y and find it to benumerically equal to 1.66 then we could be reasonably convinced that the dot at Y could be labelled as the 200 spot, and the dot at X could be labelled as 113. In this case our predicted electron beam direction is in thedirection common to the 200 and 113 planes, i.e. [03]. This particular electron diffraction pattern has a central rectangular repeat. If this is correct, further spots on this diffraction pattern can be indexed in aself-consistent manner by vector addition.Laue zoneSo far we have been looking at the central region of the diffraction pattern. This is only a part of the total diffraction pattern. If we look again at the Ewald sphere construction, we have:We have been indexing the portion in the middle with the 000 spot in it. However, there are also areas of diffraction spots at the edges of the film, caused by the Ewald sphere intersecting points in an adjacent parallel plane containing reciprocal lattice points. (If the film was small or the camera length large it is possible that it did not catch these spots at the side, so that we sometimes only have the middle part.)These outlying parts of the diffraction pattern are called Higher Order Laue Zones (HOLZs). Each of the HOLZs can be described by an equation of the general formhu + kv + hw Nwhere:∙N is always an integer, and is called the order of the Laue zone.∙[uvw] is the direction of the incident electron beam.∙hkl are the co-ordinates of an allowed reflection in the N th order Laue zone.The middle part of the diffraction pattern, with 000 in it, is the zero order Laue zone (ZOLZ), because it comes from the plane for which N =0: an allowed reflection hkl in the ZOLZ is joined to the origin 000 by a reciprocal lattice vector that lies in the ZOLZ. For the ZOLZ the electron beam [uvw] and the allowed reflection hkl satisfy the Weiss zone law hu + kv + lw= 0. The next layer up has a value N =1, then N =2, and so on, as shown.From the geometry of the way in which the Ewald sphere intersects the HOLZs, the radius of the N th HOLZ ring, R n, in reciprocal space, is given to a very good approximation by the formulaassuming that the wavelength of the electrons is much less than the modulus |uvw| of the direction [uvw] in the crystal parallel to the electron beam direction. Thus, HOLZs are seen more easily at lower voltages (e.g. 100 kV rather than 300 kV) and when the electron beam is parallel to a relatively high index direction in a crystal.It is possible to index the reflections in the HOLZs on a diffraction pattern. Examples of such indexing are given in the book Transmission Electron Microscopy of Materials by D B Williams and C B Carter.Kikuchi lines previous | next Kikuchi lines often appear on electron diffraction patterns:An example of a "two-beam" electron diffraction pattern with a number of Kikuchi lines.A pair of Kikuchi lines is arrowed.[The term "two-beam" denotes the fact that the straight-through beam, 000, and one diffraction spot are both diffracting very strongly. The intensity of all spots in this electron diffraction pattern are significantly weaker by comparison with these two beams.](Click on image to view larger version)We will not learn to index the Kikuchi lines in this TLP. Instead, we will explain their origin and behaviour with the help of the following animation.Kikuchi lines are interesting because of what they do when the crystal is moved in the beam. Diffraction spots fade or become brighter when the crystal is rotated or tilted, but stay in the same places; the Kikuchi lines move across the screen.The difference in behaviour can be explained by the position of the effective source of the electrons that are Bragg-scattered to produce the two phenomena. The diffraction spots are produced directly from the electron beam, which either hits or misses the Bragg angle for each plane; so the spot is either present or absent depending on the orientation of the crystal. The source of the electrons that are Bragg-scattered to give Kikuchi lines is the set of inelastic scattering sites within the crystal. When the crystal is tilted the effective source of these inelastically scattered electrons is moved, but there are always still some electrons hitting a plane at the Bragg angle - they merely emerge at an angle different to the one that they did before the crystal was tilted.Using polycrystalline materials in the TEM previous | next Just as with X-rays, a completely isotropic fine-grained polycrystalline sample will give a diffraction pattern of concentric rings in the zero order Laue zone (ZOLZ), as the many small crystals at random orientations produce a continuous angular distribution of hkl spots at distance 1/d hkl from the 000 spot - a ring of radius 1/d hkl around the 000 spot for each allowed reflection. The rings are then indexed according to the order of allowed reflections within the ZOLZ.As the grain size increases, the rings within the diffraction pattern break up into discontinuous rings containing discrete reflections. If there is any texture (preferred orientation) within the specimen, arcs may be seen instead of complete rings.Convergent beam electron diffraction (CBED)previous | next When a convergent beam is used instead of a parallel beam of electrons, the rays converge to a point within the specimen and come out the other side inverted like a camera. However, we do not look at the inverted image; we look at the diffraction pattern, with the spots magnified:Depending on the camera length chosen, either the zero order Laue zone can be examined or the zero order Laue zone and higher order Laue zones. Two examples of CBED images are shown below. The symmetry seen is such patterns can be related to the space group symmetry of the specimen.Examples of CBED images:Diffraction pattern showing a zero order Laue zone with a mirror in the pattern as shown(Click on image to view larger version)Diffraction pattern showing a first order Lauezone(Click on image to view larger version)Using other methods in conjunction with electrondiffraction previous | next Electron diffraction is a powerful technique - but other techniques must be used with it to put the results in context. This is a brief synopsis of how other methods can be used to help.Optical imagingThis is a very important way of analysing a specimen. Using the naked eye and optical microscopes we can determine down to a point-to-point resolution limited by the wavelength of light how many phases there are and how they relate to one another. We can also infer what type of material they are likely to be and how they may have been processed.Chemical analysisA wide range of chemical techniques can be used to find out what components are present in the different phases and in what proportions. This will narrow the field of possible elements that we need to consider when analysing ourdiffraction results. These techniques range from simple chemical tests, through infrared spectroscopy of organic samples, to a wide variety of chemical characterisation techniques that can often be performed within thetransmission electron microscope.TEM imagingUsing the TEM to image the same area of sample that is being used toproduce the diffraction pattern is an invaluable technique:Nitrided surface layer of austenitic stainlesssteel(Click on image to view larger version)Diffraction pattern from nitrided surface layer of austenitic stainless steel (Click on image to view larger version) Using the image to verify that the double dots in the diffraction pattern arebeing caused by the two crystal structures either side of the twin boundary, we can index the pattern and determine the twin plane and the crystal structures either side of it.Summary previous | next In this teaching and learning package we have considered how electron diffraction patterns are formed in the transmission electron microscope. The principles of how to index spot electron diffraction patterns have been discussed in some detail. Although we have considered how to index electron diffraction patterns from relatively simple crystal structures toillustrate the basic principles, these principles are generic and can therefore be applied to any crystal structure. We have also considered other features of electron diffraction patterns such as the formation of Kikuchi lines, the formation of convergent beam electron diffraction patterns and theformation of higher index Laue zones.。
讲义-电子衍射20130808
第四部分电子衍射谱分析方法在不同的操作条件下得到不同的电子衍射把戏，由于其衍射物理意义不同，衍射谱分析的方法也不尽相同。
最常见的电子衍射是在选区衍射的条件下得到的，是样品原子对平行电子束散射的结果。
本部分着重介绍选区衍射电子把戏分析，后面将会给出一些其它把戏的介绍，例如菊池线与背散电子衍射、汇聚束衍射。
选区电子衍射谱分析方法可以分为三种典型情况，第二和第三种情况的把戏都来自单晶衍射，由于电子束通常都有很小的束斑尺寸，当电子束照射在多晶样品的一个晶粒上，就得到了单晶衍射把戏。
〔1〕多晶衍射谱分析；〔2〕已知衍射物质和晶体结构，标定单晶衍射斑点的晶面指数；〔3〕未知物相确定和衍射把戏标定。
4.1 多晶电子衍射把戏标定方法多晶衍射把戏是一系列的同心圆，如图4-1所示。
当平行电子束照射在很多小晶体上，在物镜背焦面上就可以得到多晶衍射把戏,当参与衍射的晶体不是足够多时，就得到断断续续的圆环，这在电子衍射谱中更为常见。
每一个圆环是由晶面间距相同的晶面衍射得到的，圆环半径与晶面间距存在关系R d = Lλ。
多晶把戏的标定就是确定每个圆环对应的晶面族指数。
图4-1 典型的多晶衍射把戏4.1.1 N比值法对于立方结构晶体，其低指数晶面存在确定的比例关系，可以用N比值法标定多晶衍射把戏。
像铁、铜、金、银等大部分的金属都属于简单立方结构。
N比值法把戏标定步骤如下：1.测量圆环直径并计算半径R；2.计算R2，求R i2/R12，必要时x2或者x33.假设有R12：R22：R32：R42：R i2符合以下关系，说明是立方晶系结构，根据公式h2 + k2 + l2 = N2就可以写出相应晶面族指数，也可以查对表4-1找到相应的hkl。
1：2；3：4：5：6：8：9：10:11 简单立方3：4：8：11：12：16：19：20：24：27 面心立方2：4：6：8：10：12：14：16：18：20 体心立方3：8：11：16：19：24：27：32：35：40 金刚石1：3：4：7：9：12：13：16：19：21 六方晶系电子衍射分析时需要精确测定相机常数，最常用的方法就是利用多晶金表样，获取多晶衍射环，因为金各个晶面指数对应的镜面间距是知道的，根据关系R d = Lλ可以计算相机常数，其中d是晶面间距标准值，可查PDF得到。
电子衍射 (2)
则有：
（二）晶体的衍射花样
晶胞：晶体结构中的基本重复单位叫做晶胞。将三 维晶体恰当地(对称性、体积最小性)划分成一个个 完全等同的平行六面体，叫晶胞。 晶胞参数（晶格常数）： a、b、c、 、 、
a
c
p(x,y,z)
b
晶面（晶面族）：通过原子中心的平面称为晶面，一组组平行平面称为晶面族。 M
3
晶面指数（密勒指数）： 某晶面在三个晶轴上的截距分别是h′a、k′b、l′c。 (a,b,c为单位长度）其中h′k′l′是晶面在晶轴上的 截数。
h′a
M1
M
3
c l′c b
M
a
O
2
k′b
晶
电子束（X射线）具有一定的波长，根据布喇格定律， 当相邻两晶面上反射电子束（X射线）（如图中的I、II线） 的程差Δ符合下述条件时，可产生相长干涉。
实验内容与方法
普朗克常数公认值
数 据 表 格
Ag的晶格常数a = 4.0862A
（1）电源 开机前必须检查高压旋钮是否旋至最低。开机后预热 半分钟即可正常工作。 （2）聚焦 调节衍射管第二阳极电压，是衍射图样清晰。 （3）辅助聚焦 调节衍射管第三阳极电压，使衍射图样更清晰。 （4）x位移 x轴向移动电子束，使用时可根据需要改变衍射图样 的位置，以延长电子衍射管的寿命。 （5）y位移 y轴向移动电子束，功能同x位移。 （6）亮度 调节荧光屏上的衍射图样亮度。 （7）高压 顺时针方向升高电压，逆时针方向降低电压。
于是，有
所以有
亦即各衍射圆环的半径的平方之比等于各衍射圆环对应的晶 面的米勒指数平方和之比。 知道了各个电子衍射圆环的半径，就可以根据下表得到 各个圆环所对应的Mn。可见指数定标过程就是用实验测得的 衍射环半径的数据之平方，找出一列最简单的整数关系。
材料分析教学课件-第4章 电子衍射
• 只有当F (hkl） ≠ 0时，才能保证得到衍射束。 • 所以 F (hkl） ≠ 0是产生衍射束的充分条件。
3. 结构因素
结构因数F（hkl）是描述晶胞类型和衍射强度之间关系的
一个函数。结构因素的数学表达式为
N
F(hkl) f j exp[ 2i(hx j kyj lz j )] j 1
当h, k, l 为全偶, 全奇时 F= 4 f 当h, k, l为奇，偶混合时 F = 0
I 16 f 2
I=0
面心晶胞 h k l 为全偶，全奇时，衍射强度不为零
h k l为奇偶混合时，消光.
(5) 六方晶胞
密排六方单胞，在最简单的情况下单胞中有两个同种原子，
坐标分别为 000 和 1，2 其1 结构因数为 332
2 d sin
n
n次衍射的解释
d
d/2
n=2的假想晶面
衍射角θ的解释
2d sin
sin
2d
通常λ≤ 0.002nm d 在1nm左右
•所以Sinθ很小，也就是入射角θ很小. •入射束与衍射晶面稍有角度就能产生衍射.
二. 埃瓦尔德图解：
• 埃瓦尔德图解是布拉格方程的几何 表达式。利用埃瓦尔德图解可以直观地 看出：
cosc*c
1
a*
1 a c osa* a
b*
1 b c osb*b
c*
c
1 cosc*c
特例： 在直角坐标系中正.倒空间基矢量的关系
直角坐标系：立方晶系，四方晶系，正交晶系
a*∥a, b*∥b, c*∥c
a*=1/a ， b*=1/b, c*=1/c
g
在倒易空间中，任意矢量的大小和方向
电子衍射-PPT
❖ 通常电子衍射图的标定过程可分为下列三种情况:
1)已知晶体(晶系、点阵类型)能够尝试标定。 2)晶体虽未知,但依照研究对象估计确定一个范围。就在这
些晶体中进行尝试标定。 3)晶体点阵完全未知,是新晶体。此时要通过标定衍射图,来
确定该晶体的结构及其参数。所用方法较复杂,可参阅电 子衍射方面的专著。
征之因此区别X射线的主要原因。
8-2 偏离矢量与倒易点阵扩展
❖ 从几何意义上来看,电子束方向与晶带轴重合时,零层倒易 截面上除原点0*以外的各倒易阵点不估计与爱瓦尔德球相 交,因此各晶面都可不能产生衍射,如图(a)所示。
❖ 假如要使晶带中某一晶面(或几个晶面)产生衍射,必须把 晶体倾斜,使晶带轴稍为偏离电子束的轴线方向,此时零层 倒易截面上倒易阵点就有估计和厄瓦尔德球面相交,即产 生衍射,如图(b)所示。
量。
倒易点阵扩展
❖ 下图示出偏离矢量小于零、等于零和大于零的三种情况。 如电子束不是对称入射,则中心斑点两侧和各衍射斑点的 强度将出现不对称分布。
8-3 电子衍射基本公式
❖ 电子衍射操作是把倒易点阵的 图像进行空间转换并在正空间 中记录下来。用底片记录下来 的图像称之为衍射花样。右图 为电子衍射花样形成原理图。
❖ Rdhkl=f0·MI·Mp·λ=L＇λ ❖ 称Lˊλ为有效相机常数
选区衍射
❖ 选区衍射就是在样品上选择一个 感兴趣的区域,并限制其大小,得 到该微区电子衍射图的方法。也 称微区衍射。
❖ 光阑选区衍射(Le Poole方式) 此法用位于物镜像平面上的光阑 限制微区大小。先在明场像上找 到感兴趣的微区,将其移到荧光 屏中心,再用选区光阑套住微区 而将其余部分挡掉。理论上,这 种选区的极限≈0、5μm。
电子衍射原理与分析课件
05
电子衍射在生物学中的 应用
大分子结构分析
蛋白质晶体学
电子衍射技术在大分子结构分析中发挥 着重要作用，尤其在蛋白质晶体学领域 。通过电子衍射，可以解析蛋白质晶体 的空间结构，为理解蛋白质功能和设计 新药物提供关键信息。
当电子束以一定能量和方向入射 到晶体或非晶体材料上时，会发 生衍射，即电子的运动轨迹发生
弯曲。
衍射现象可以通过布拉格方程（ nλ=2dsinθ）进行描述，其中λ 为入射电子波长，d为晶面间距
，θ为衍射角。
电子衍射与X射线衍射的区别
电子衍射的波长比X射线短， 因此具有更高的分辨率和灵敏 度，能够更准确地测定晶格常 数和晶体结构。
膜蛋白分析
电子衍射还可以用于分析生物膜上的 膜蛋白，如通道蛋白和转运蛋白。这 些蛋白在物质跨膜运输和信号转导过 程中发挥关键作用。
病毒形态与结构分析
病毒形态描述
通过电子衍射技术，可以详细描述病毒的形 态和大小，这对于病毒分类、鉴定和疫苗设 计具有重要意义。
病毒结构解析
病毒的结构通常由蛋白质外壳和内部的核酸 组成。电子衍射技术可以解析病毒的精细结 构，揭示其组装机制和感染机制，为抗病毒 药物的设计提供理论支持。
THANKS FOR WATCHING
感谢您的观看
扫描电子显微镜(SEM)
总结词
扫描电子显微镜是利用电子束扫描样品表面，通过收集和分析二次电子、反射电子等信号来观察样品 表面形貌和特征的实验方法。
详细描述
扫描电子显微镜具有较高的空间分辨率和放大倍数，能够观察样品表面的细微结构和形貌变化。在实 验过程中，需要对样品进行镀金或碳涂覆等处理，以增加导电性和二次电子信号的收集效率。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
若样品内某(hkl)晶面满足布拉格条件，则在 与入射束呈2θ角方向上产生衍射。
透射束和衍射束分别与离试样L处的照相底片 相交于O’和P’点。
O’点：透射斑点000 P’点：衍射斑点hkl
若照相底片上中心斑点到衍射斑点的距离为R
R = tan2θ L
电子衍射时，满足布拉格定律的角度θ很小，故
代入布拉格公式2dsinθ=λ可得：
rd = f0λ
由于底片上（或荧光屏上）记录到的衍射花样 是物镜背焦面上第一幅花样的放大像。若中间镜 与投影镜的放大倍率分别为Mi和Mp。则底片上相 应衍射斑点与中心斑点的距离R应为
R = rM iM p
因为
(R / M iM p )d = λfo
(a) 第一幅衍射花样的形成和选 区电子衍射原理
爱瓦尔德球
L、λ、R均已知，故可求 出晶面间距d，晶面夹角。
Rd = Lλ R可在衍射
谱上量出
利用电子衍射谱进行
L
结构分析的依据。
衍射花样
晶体结构、位向
入射 束
O
试样
1 λ 2θ 1 λ
1d
G
倒易 点阵
底板
O' R P'
相机常数为某一定值，所以R反比于d。由此可见，在电子衍射中， 晶体参数d与衍射斑点R之间的关系比Ｘ射线衍射中相应的关系简单。
目前，先进的透射电子显微镜都有自动电子补偿器消除相对磁转 角，为在显微图像上显示出晶体学方向提供了便利。
4.4 倒易点阵平面及其画法
电子衍射花样
倒易点阵与Ewald球面相截的 部分，再在荧光屏上投影。
单晶的电子衍射谱是一个二 维倒易平面的放大。
衍射斑点与倒易阵点的配 置完全相似。
掌握二维倒易点阵平面的性质 及画法对于熟练分析电子衍射 谱是必须的。
所以
R = L = λL gk
R = (λL)g
R = λL d
r R
=
(λL) gr
是电子衍射几何分析的另一种
表示方式。
r R
=
(λL) gr
衍射斑点R矢量就是产生这一斑点 晶面组的倒易矢量g的比例放大。
对单晶样品而言，衍射花样就是落在爱瓦 尔德球球面上所有倒易阵点中满足衍射条 件的那些倒易阵点所构成图形的放大像。
正空间
r [uvw ]
(h3k3l3 ) (h2k2l2 )
hu + kv + lw = 0
电子衍射谱分析常用的晶带定律
(uvw)* ⊥ [uvw]
h1u + k1v + l1w = 0 h2u + k2v + l2 w = 0
倒空间
g2
(h3k3l3 )g3 000
(h1k1l1 )
(h2k2l2 ) g1 (h1k1l1)
(h1k1l1 )
倒空间
g2 (h2k2l2 )
(h3k3l3 )g3
g1 (h1k1l1)
000
(uvw)*
晶带正空间与倒空间对应关系图
g = ha * +kb * +lc * r = ua + vb + wc
g⊥r
u, v, w晶带轴的指数（正点阵中晶向指数） h, k, l倒易点阵矢量指数（正点阵中晶面指数）
则
Rd = λfoM iM p
我们定义 L' = foM iM p 为“有效相机长度”
式中L’并不直接对应于样品至照相底片的实际距离。
f0、Mi、Mp分别取决于物镜、中间镜和投影镜的激磁电流，因而有效 相机常数也将随之变化。为此，我们必须设法使三个透镜的电流固定，在 这一条件下来标定仪器的相机常数，使R和1/d之间保持确定的比例关系。
tan 2θ ≈ 2θ R = L tan 2θ
sinθ ≈ θ 2d sinθ = λ
R = 2Lθ
λ = 2dθ
Rd = Lλ
L称为相机常数或相机长度
λ和d的单位：nm；L和R的单位：mm。
电子束的波长λ和样品到照相底片的距离L是由衍射条件确定的，在 恒定实验条件下，Lλ是一个常数，称为衍射常数。
利用爱瓦尔德球构图推导电子衍射几何分析公式可进一步说明 电子衍射花样的物理意义。
因为 2θ很小，使发生衍射的晶面（hkl）近 似平行于入射束方向，或者说其倒易矢量g （∥Nhkl）近似垂直于入射波矢量k，而底片上斑 点P′的坐标矢量R =O’P’也垂直于入射束方向。
于是近似有 △OO*G∽△ OO’P’
物镜、中间镜、投影镜磁场的作用，使电子束除了径向折射以外， 还使其绕光轴转动，产生磁转角，以致使斑点R矢量与衍射晶面的法线方 向（即g方向）之间不再保持近似平行关系。为了确定在某一相机长度和 放大倍率下衍射花样与形貌图像的相对磁转角，通常选择外形特征可以 直接反映晶体学方向的MoO3晶体作为标定磁转角的标样。
单晶花样中的斑点可以直接被看成是相应 衍射晶面的倒易阵点，各个斑点的R矢量也 就是相应的倒易矢量g。
因此，两个衍射斑点坐标矢量R之间的夹角 就等于产生衍射的两个晶面之间的夹角。
在透射电子显微镜中是如何得到电子衍射花样的？
利用薄透镜的性质，可从几何 上来说明在物镜背焦面处形成第 一幅衍射花样的过程。
(1)未被样品散射的透射束平 行于主轴，通过物镜后聚焦在主轴 上的一点，形成 000中心斑点；
(2)被样品中某(hkl)晶面散射 后的衍射束平行于某一副轴，通过 物镜后将聚焦于该副轴与背焦平 面的交点上，形成hkl衍射斑点。
1
由于通过透镜中心的光线不发生折射，则有： r = f0 tan2θ式中ƒo是物镜的ຫໍສະໝຸດ 距，r是hkl斑点至000斑点的距离。
爱瓦尔德球
入射 束
O
试样
2θ 1 λ
1d
G
倒易 点阵
底板
O' R P'
4.4.1 晶带定律（Weiss zone law）
许多晶面族同时与一个晶体学 方向[uvw]平行时，这些晶面族总称 为一个晶带，[uvw]称为晶带轴。
正空间
r [uvw ]
(h3k3l3 ) (h2k2l2 )
因为属于同一晶带的晶面 族都平行于晶带轴方向，故倒 易矢量g⊥r， r·g =0，构成一个 与晶带轴方向正交的二维倒易 点阵平面(uvw)*。
(uvw)*
可解出晶带轴方向[uvw]如下：
u = k1 l1
k2 l2
v = l1 h1
l2 h2
w = h1 k1
h2 k2
u : v : w = (k1l2 − k2l1 ) : (l1h2 − l2h1 ) : (h1k2 − h2k1 )
正空间的一个晶面族(hkl)可用倒空间的一个倒易点hkl来表示， 正空间的一个晶带[uvw]可用倒空间的一个倒易面(uvw)*表示，大大方 便了电子衍射谱的分析。