- 00:08Descripción
- 01:08Principles of X-ray Diffraction
- 04:43Instrument, Sample and Beam Parameters
- 05:57Selection of the Parameters for the Acquisition
- 06:24Acquisition and Analysis
- 07:04Resultados
- 07:48Applications
- 08:58Summary
X 射线衍射
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Descripción
资料来源：佐治亚州佐治亚州理工学院材料科学与工程学院费萨尔·阿拉姆吉尔，佐治亚州亚特兰大
X射线衍射（XRD）是材料科学中用于测定材料原子和分子结构的技术。这是通过用事件 X 射线照射材料样本，然后测量材料散射的 X 射线的强度和散射角度来实现的。散射 X 射线的强度绘制为散射角的函数，材料的结构根据位置、角度和散射强度峰的强度进行分析来确定。除了能够测量晶体中原子的平均位置外，还可以确定实际结构如何偏离理想结构（例如来自内部应力或缺陷）的信息。
X射线的衍射是XRD方法的核心，是一般X射线散射现象的子集。XRD 通常用于表示可以广角 X 射线衍射 （WAXD），属于使用弹性散射 X 射线波的几种方法。其他基于弹性散射的 X 射线技术包括小角度 X 射线散射 （SAXS），其中 X 射线在样本上通常偏射在 0.1-100的小角度范围内。SAXS 测量几纳米或更大（如晶体上部结构）的尺度的结构相关性，以及测量薄膜厚度、粗糙度和密度的 X 射线反射率。WAXD覆盖的角度范围超过100。
Principios
衍射峰位置与晶体结构的关系：
当波长足够小的光波在晶格上发生时，它们会从晶格点衍射。在某些入射角度，衍射平行波建设性地干扰并产生可探测的强度峰值。W.H. Bragg 确定了图 1 所示的关系，并推导出了相应的方程：
n = = 2dhkl辛 [ 1]
此处 * 是使用的 X 射线的波长，dhkl是具有（hkl） Miller 指数* 的特定平面集之间的间距*，而α是测量衍射峰的发生率角。最后，n 是表示衍射的”谐波顺序”的整数。例如，在n=1，我们有第一次谐波，这意味着X射线通过晶体（相当于2dhkl sin）的路径正好是1μ，而在n=2，衍射路径是2°。我们通常可以假设 n=1，通常 n=1 表示[lt; sin-1（2+/dh’k’l’）]，其中 h’k’l’是显示衍射实验中第一个峰值（在最低 2° 值）的平面的 Miller 索引。Miller 指数是一组三个整数，构成用于识别晶体中方向和平面的符号系统。对于方向，[h k l] Miller 指数表示沿方向的两个点的分别 x、y 和 z 坐标（在笛卡尔坐标系中）的正一点差。对于平面，平面的 Miller 指数（h k l）只是垂直于平面方向的 h k l 值。
在反射模式下的典型 XRD 实验中，X 射线源固定在位，样品相对于 X 射线光束旋转超过 α。探测器拾起衍射光束，必须以两倍速率旋转，以±的速度保持样品旋转（即，对于给定的样品角度 α，探测器角度为 2°）。实验的几何形状如图 1 所示。
图1：布拉格定律的例证。
当观察到强度的峰值时，方程 1 必然满足。因此，我们可以根据观测这些峰值的角度计算 d 间距。通过计算多个峰的 d 间距，可以使用数据库（如 Hanawalt 搜索手册）或使用的 XRD 软件数据库库来识别晶体类和晶体结构参数材料样本。
我们将假设正在调查的样品不是一个晶体。如果样本是具有与样品表面平行的特定（h_k_l_）平面的单一晶体，则需要旋转，直到满足（h_k_l_）的布拉格条件，才能看到衍射强度（n=1）的峰值，其谐波（h_k_l_）峰值（例如 n=2）在较高角度也能检测到。在所有其他角度，单个晶体样品中没有峰值。相反，让我们假设样品是多晶或粉末，具有统计上显著数量的晶体颗粒或粉末颗粒由事件X射线束照亮。在此假设下，样本由随机定向颗粒组成，所有可能的晶格平面具有类似的统计概率。
dhkl 和单位细胞参数之间的关系如下，公式 2-7 用于 7 个晶体类、立方、四角、六边形、菱形、胸腔、单临床和三临床。单位单元参数由 7 个晶体类的单位单元边缘的长度 （a、b、c）和角度 （*、 *、 *） 组成（图 1x 显示了其中一个晶体类的示例：a_b_c 和 +=====900）的四角结构。使用多个衍射峰值位置（即几个不同的dhkl值），可以唯一求解单位单元参数的值。
图2：四角结构为七种晶体类之一。
立方 （a = b = c; = = = = = = = 900）：
[2]
四联体 （a = b + c; √ √ √ √ √ √ √ √ 900）：
[3]
六角形 （a = b + c; = = = = 900;= 1200）：
[4]
奥索霍比奇 （a + b + c; √ √ √ √ √ √ √ √ 900）：
[5]
隆博面体 （a = b + c; √ √ √ √ √ √ √ √ √ ） 900）：
[6]
单体诊所 （a = b + c; √ √ √ √ √√ √ √ √ √ √ √ √ ）
[7]
三联诊所 （a + b + c; # # + + + + = = 900）：
[8]
衍射峰强度与晶体结构的关系：
接下来，我们研究XRD模式中导致强度的因素。这些因素可以分解为 1） 直接来自材料的独特结构方面（结构中散射原子的特定类型和位置）和 2） 对材料不特定于材料的贡献。在前者中，有两个因素：”吸收因子”和”结构因素”。吸收因素主要取决于材料在进出时吸收X射线的能力。只要样品不薄（样品应比 X 射线的衰减长度厚 3 倍），此因子就不存在依赖性。换句话说，吸收因子对不同峰的强度的贡献是恒定的。”结构因子”直接影响特定峰的强度，这是结构的直接结果。其余因子”多重性”，它占属于同一族的所有平面，因为它们是对称相关的，而来自 XRD 实验几何体的”洛伦兹-极化”因子也影响峰的相对强度，但它们不是材料所特有的，并且可以很容易地用分析表达式来解释（即XRD分析软件可以去除它们与分析功能）。
图3：三衍射射线路径，其中光线11’和22’满足布拉格条件，而射线33’的结果是由原子（红色圆圈）在任意位置散射的结果。
作为材料对XRD峰的相对强度的独特结构贡献的唯一因素，结构因子非常重要，需要仔细观察。在图 2 中，我们假设第1阶布拉格衍射条件（请记住，这对应于 n_1）在光线11′和射线22′之间得到满足，它们分散在 h00 方向的两个原子平面上（使用前面描述的 Miller 指数表示法）相隔一个距离 d。在此条件下，射线11′和射线22′之间的路径长度差为 ±（22′-11’） = SA = AR = = = 。因此，衍射射线1和2之间的相移是±22′-11′ =（+（22′-11’）/+） 2= = 2°（假设立方对称，因此，d = h00 方向的a/h]。
在分析几何学中，通过几个步骤可以显示，相移（[33′-11′]）与射线3衍射的任意对象原子的任意平面，间隔任意距离x，由：[（33′-11’） ]2°hu，其中u_x/a（a是（h00）方向的单位单元参数。以其他两个正交方向（0k0）和（00l）和v_y/a和w_z/a作为y-和z方向中的小数坐标，相移的表达式延伸到+2°（hu_kv_lw）。现在，由j-th原子分散在单元单元中的X射线波将有一个散射振幅fj和一个相位=j，这样描述它的函数就是
。因此，我们寻求的结构因子是单元单元中所有唯一原子的所有散射函数的总和。此结构因子 F 给出如下：
[9]
结构因子贡献的强度因子为I=F2。
根据特定平面（h，k，l）原子的位置（u，v，w），存在存在建设性、破坏性或中间的散射波之间的干扰，这种干扰直接影响XRD峰的振幅代表（hkl）平面。
现在，强度图，I，与2°是XRD实验中测量的。晶体类型和相关单位单元参数（a、b、c、α、α和α）的确定可以通过观察系统存在/峰缺失、使用方程 2-9、将值与数据库进行比较、使用推导和消除过程来进行分析。如今，这个过程是相当自动化的各种软件链接到晶体结构数据库。
Procedimiento
Resultados
In Figure 4 we see the XRD peaks for the Ni powder sample. Note that the peaks that are observed (e.g. {111}, {200}) are for those that have either all even or all odd combinations of h, k, and l. Ni is face-centered cubic (FCC), and in all FCC structures, the peaks corresponding to {hkl} planes where h, k, and l are mixtures of even and odd integers, are absent due to the destructive interference of the scattered X-rays. Peaks corresponding to planes, such as {210} and {211} are missing. This phenomenon is called the systematic presence and absence rules, and they provide an analytical tool for assessing the crystal structure of the sample.
Figure 4: An XRD scan of Ni with a face-centered cubic structure is shown.
Applications and Summary
This is a demonstration of a standard XRD experiment. The material examined in this experiment was in a powder form, but XRD works equally well with solid piece of material as long as the sample has a flat surface that can be set parallel to the plane of the sample stage.
XRD is a fairly ubiquitous method for determining the presence (or absence) of crystallographic order in materials. Beyond the standard application of determining the crystal structure, XRD is often used to obtain a variety of other structural information such as:
- Whether or not the structure of a material is amorphous (characterized by a broad hump in the diffraction intensity and a lack of discernable crystallographic peaks),
- Whether the sample is a composite material consisting of multiple crystallographic phases and, if so, determine the fraction of each phase,
- Determining whether a material is an amorphous/crystalline composite
- Determining the grain/particle size of the material,
- Determining the degree of texture (preferred orientation of grains) in material.
Transcripción
X-Ray diffraction is a technique used to determine the atomic and molecular structure of materials. Solids have a crystalline structure, which corresponds to a microscopic arrangement of atoms that is repeated periodically. By staking planes, a 3-D structure of specific symmetry can be formed.
These structural arrangements result in a specific packing geometry that dictates the physical and chemical properties of the material. Such as magnetization, thermal conductivity, or malleability. Reflecting x-rays off of materials can reveal the inner details of their structure.
This video will illustrate the general principles of x-ray diffraction on a material and how this phenomenon is used in the laboratory to determine the structure and chemical composition of materials.
To begin, let’s have a closer look at a crystal. It is formed of atomic lattices disposed in planes periodically separated by a distance dhkl of a few angstroms. H, k, l are Miller indices, a set of three integers the constitute a notation system for identifying directions and planes within crystals. The smallest repeating structure in a crystal is called the unit cell. Different angles, alpha, beta, gamma, and lengths a, b, c, of a unit cell forming the lattice will give rise to different symmetries. There are seven crystal systems. Cubic, tetragonal, orthorhombic, rhombohedral, monoclinic, triclinic, and hexagonal.
The relationship between the unit cell parameters and the Miller indices can be calculated for each crystal class. Electromagnetic of wavelength lambda can have similar dimensions with the differences between planes within the crystal’s lattice. These correspond to wavelengths in the x-ray spectral range. When x-ray light waves irradiate a crystal at an incident angle theta, they propagate through the crystal and encounter lattice points from which they defract. Bragg’s Law relates these parameters where n is an integer that represents the harmonic order of the diffraction. For a given lambda, only specific angles theta give rise to diffraction. This is the unique signature of a crystalline structure.
In an experiment, the sample is rotated and the detector that collects the scattered x-rays records peaks in intensity when reaching these characteristic angles. One can then extract the lattice spacing DHKL for each angle satisfying the Bragg’s Law. Using multiple diffracted peak positions corresponding to several distinct DHKL values, the parameters of the unit cell can be solved uniquely.
Two main factors contribute to the relative intensity of the peaks. First, there are the non-structural contributions, which include the ability of the material to absorb x-ray light, and the geometry of the XRD experiment. These can be taken into account in the post-processing of the experimental data. Second, and most importantly, the structural contribution of the material is carried to the relative intensities of XRD. Each diffraction peak is in fact the sum of all the scattered amplitudes from multiple ray paths diffracted by all the unique atoms in a unit cell. If scattered lights are in phase, there is constructed interference. While if they are out of phase, there is destructed interference. These interferences directly affect the amplitude of the XRD peaks, representing the HKL planes of the crystal.
We will now see how these principles apply in an actual x-ray diffraction experiment.
Before starting, carefully inspect the XRD instrument and assess its status and safety. XRD users must be trained in basic radiation safety before having access to the instrument. Then proceed with sample preparation. In this experiment, we use a nickel powder sample in the form of a pressed pellet.
It is important that the sample is not thin and it should be at least three times thicker than the attenuation length of the x-rays. Note that the following procedure applies to a specific XRD instrument and its associated software and there may be some variations when other instruments are used.
Load the sample in the sample spinner stage and lock the sample into position, making sure the irradiated side of the sample is parallel to the sample stage. Use a mask to adjust the x-ray beam size of the instrument according to the sample diameter. At the smallest incident angle, the beam must have a footprint smaller than the sample width.
Now it is time to choose the acquisition parameters. First, select the angle range for the XRD scan. Typically, the range goes from 15 to 90 degrees. Then, select the degree step size as well as the integration time at each angle scanned.
Next, proceed to the data acquisition. After the scan, a graph of the intensity as a function of the angle to theta is obtained. From this initial scan, select specific peaks and determine peak positions.
Repeat the acquisition and focus this time on a narrower scan range around specific peaks. Using a smaller step size in angle to obtain higher resolution data. Once the data acquisition is finished, data can be analyzed to identify the structure of the material.
Using the instrument software and database library, each peak of the spectrum is identified and associated to a specific symmetry of crystal arrangement. In this particular case of the nickel powder sample, the spectrum shows a first peak corresponding to a one one one symmetry.
The second peak is associated to a two zero zero symmetry and so on. Then the software determines that this specific combination of symmetries corresponds to a face centered cubic structure and it identifies that the sample is a nickel powder.
X-ray diffraction is a standard method for determining the presence or absence of crystallographic order in materials. It is often used to obtain a variety of other structural information regarding internal stress and defects in a crystal, or multiple crystallographic phases in composite materials. XRD technique is also used in biology to determine the structure and spatial orientation of biological macromolecules such as proteins and nucleic acids.
In particular, this is how the double helix structure of DNA has been discovered, leading to the Nobel Prize in Physiology or Medicine in 1962. The study of the geochemistry of minerals either for mining purposes or even for planetary exploration also makes use of XRD technique. Think of the Rover Curiosity on Mars that has amongst its ten scientific instruments an XRD detector to analyze the composition of the martian soil.
You’ve just watched Jove’s introduction to x-ray diffraction. You should now understand the crystalline structure of a solid and the principles of x-ray diffraction. You should also know how the XRD technique is used in the laboratory to obtain the structure and chemical composition of materials.
Thanks for watching!