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Theory and principles  理论和原则

This chapter will briefly present the analytical techniques IC and ICP-OES. In addition, an in-depth account of X-ray diffractometry will be presented.
本章将简要介绍 IC 和 ICP-OES 分析技术。此外,还将深入介绍 X 射线衍射仪。

3.1 X-ray diffraction 3.1 X 射线衍射

The theory of X-ray diffraction is well-known (see for example Pecharsky et al. (2009)). The following theory is just a brief summary of what one might encounter in the literature, unless otherwise stated.
X 射线衍射理论是众所周知的(参见 Pecharsky 等人 (2009))。除非另有说明,以下理论只是对文献中可能出现的理论的简要总结。

3.1.1 Analytical principle
3.1.1 分析原理

The principle of x-ray diffractometry relies on the fundamental interaction between electromagnetic (EM) radiation and matter, and on wave-wave interaction. A wave hitting an obstacle will diffract; that is, bend around the obstacle. The bending effect varies depending on the wave’s wavelength, and the size of the obstacle. Visble light will not be diffracted by atoms in a crystal, to any observable extent, because the wavelength is so much longer than the distance between the atoms.
X 射线衍射测量法的原理依赖于电磁辐射与物质之间的基本相互作用以及波与波之间的相互作用。波碰到障碍物会发生衍射,即绕着障碍物弯曲。弯曲效果因波的波长和障碍物的大小而异。可见光不会被晶体中的原子衍射到任何可观察到的程度,因为波长比原子间的距离要长得多。
When two waves are superimposed, they will interfere with each other. The amplitudes will add double if their maxima are perfectly aligned (constructive interference) and cancel each other if their minima are perfectly aligned (destructive interference). This is visualized in Figure 3.1. Constructive interference is central to the principle of X-ray diffraction.
当两个波叠加在一起时,它们会相互干涉。如果它们的最大值完全一致(建设性干涉),振幅会加倍;如果它们的最小值完全一致(破坏性干涉),振幅会相互抵消。如图 3.1 所示。建设性干涉是 X 射线衍射原理的核心。
EM-radiation can interact with matter in three ways: ionization, compton scattering, and thomson scattering. Ionization: If the electron hit by X-rays are ejected out of the
电磁辐射可以通过三种方式与物质相互作用:电离、康普顿散射和汤姆逊散射。电离:如果被 X 射线击中的电子被弹射出

Figure 3.1. Contructive interference occurs when the peaks of the superimposed waves overlap, while destructive interference occurs when the minima overlap. Figure taken from Fundamentals of Powder Diffraction and Structural Characterization of Materials, 2nd ed., by V. K. Pecharsky and P. Y. Zavalij, 2009, New York, USA: Springer. Copyright 2009 by Springer Science+Business Media. Adapted with kind permission from Springer Science+Business Media.
图 3.1.当叠加波的峰值重叠时会产生破坏性干涉,而当极小值重叠时会产生破坏性干涉。图摘自《粉末衍射与材料结构表征基础》,第 2 版,作者 V. K. Pecharsky 和 P. Y. Zavalij,2009 年,美国纽约:施普林格出版社。版权归 Springer Science+Business Media 2009 所有。经 Springer Science+Business Media 许可改编。

Figure 3.2. Showing X-rays hitting an electron, which then re-emits the wave without any energy loss. In three dimensions, the emitted wave will be spherical. Figure taken from Fundamentals of Powder Diffraction and Structural Characterization of Materials (p. xx), 2nd ed., by V. K. Pecharsky and P. Y. Zavalij, 2009, New York, USA: Springer. Copyright 2009 by Springer Science+Business Media. Adapted with kind permission from Springer Science+Business Media.
图 3.2.显示 X 射线击中电子后,电子在不损失任何能量的情况下重新发射出波。在三维空间中,发射的波是球形的。图摘自《粉末衍射和材料结构表征基础》(第 xx 页),第 2 版,作者 V. K. Pecharsky 和 P. Y. Zavalij,2009 年,美国纽约:施普林格出版社。版权归 Springer Science+Business Media 2009 所有。经 Springer Science+Business Media 许可改编。

atom, the atom has become ionized. In this process, the wave’s energy is fully transferred to the electron. This is a type of inelastic interaction, because energy transfer is involved. Compton scattering: The photon may transfer some of its energy to the electron, and being scattered at an angle. This is also an inelastic interaction. The events following the interaction may involve a fully ejected electron, or just an excitation. Thomson scattering: the wave may interact elastically, and induce oscillations in the electron at the frequency of the incoming radiation. The electron then emits EM radiation in all direction, conserving the energy. It is this elastic scattering that is interesting in X-ray diffraction.
原子电离。在这个过程中,波的能量完全转移到了电子上。这是一种非弹性相互作用,因为其中涉及能量转移。康普顿散射:光子可能会将部分能量转移给电子,并以一定角度散射。这也是一种非弹性作用。相互作用后发生的事件可能是电子完全射出,也可能只是激发。汤姆逊散射:波可能会发生弹性相互作用,并在电子中引起与传入辐射频率相同的振荡。然后,电子向各个方向发射电磁辐射,保存能量。这种弹性散射在 X 射线衍射中非常有趣。
In three dimensions, the elastically scattered wave is spherical, with its origin in the scatter point (see Figure 3.2). If five such scatter points (electrons) are placed next to each other, and are irradiated, the emitted and spherical waves will interfere at certain points, both constructivelly and destructivelly. See Figure 3.3
在三维空间中,弹性散射波是球形的,其原点位于散射点(见图 3.2)。如果将五个这样的散射点(电子)相邻放置并进行照射,发射波和球面波将在某些点发生干涉,既有建设性干涉,也有破坏性干涉。见图 3.3
Building on the basic theoretical foundation that P.P. Ewald developed in the beginning of the 1900’s, Max von Laue and coworkers discovered that a crystal lattice works as a three dimensional diffraction grating when irradiated by X-rays. In an experimental set-up they bombarded a single crystal of copper sulphate with X-rays and placed a photographic plate behind the crystal. They observed a strong central darkening, due to the primary beam, and several other dots surrounding the center (the so-called “Laue
在 P.P. Ewald 于 1900 年代初提出的基本理论基础上,Max von Laue 及其同事发现,晶体晶格在 X 射线照射下可产生三维衍射光栅。在一个实验装置中,他们用 X 射线轰击硫酸铜单晶体,并在晶体后面放置一个照相板。他们观察到,由于主光束的作用,晶体中央出现了一个强烈的暗点,而中心周围则出现了其他几个点(即所谓的 "Laue

dots”). Thus, the diffraction of X-rays by crystals was discovered, and Laue recieved the Nobel Price in 1914 for this discovery.
点")。劳厄因此获得了 1914 年的诺贝尔奖。
Within a year of Laue’s discovery, William Lawrence Bragg realized that the diffracted X-rays could be modeled as X-rays reflecting off parallel planes within the atom (Ewald 1962, Chapter 5), and derived a geometrical criterion for when constructive interference would occur. The unit cell parameters in a crystal (distances between atoms in the unit cell) are (very much) characteristic for the crystal lattices, and so the diffraction of X-rays by crystals could be used to deduce the crystal structure of crystalline materials. The Braggs derived a geometrical relationship defining the angles at which scattered waves would interfere constructively and produce an intense “reflection” of the x-rays. This relationship, termed “Bragg’s law”, is central to the x-ray diffractometer.
在劳厄发现 X 射线衍射的一年之内,威廉-劳伦斯-布拉格(William Lawrence Bragg)意识到衍射的 X 射线可以被模拟为原子内部平行平面反射的 X 射线(Ewald,1962 年,第 5 章),并推导出何时会发生建设性干涉的几何标准。晶体中的单胞参数(单胞中原子间的距离)是晶格的(非常)特征,因此晶体对 X 射线的衍射可用于推断晶体材料的晶体结构。布拉格夫妇推导出一种几何关系,定义了散射波发生建设性干涉并产生强烈 X 射线 "反射 "的角度。这种关系被称为 "布拉格定律",是 X 射线衍射仪的核心。
To derive Bragg’s law, we model the crystal lattice as a structure consisting of various “atomic planes”. At these planes, the electron density is higher than in-between the planes, and the probability of scattering of the incoming X-rays is higher. The distance between two adjacent planes is denoted d d dd, the X-ray’s wavelength is denoted λ λ lambda\lambda, and the incident irradiation angle is denoted θ θ theta\theta. All this is visualized in Figure 3.4.
为了推导出布拉格定律,我们将晶格建模为由各种 "原子平面 "组成的结构。在这些平面上,电子密度比平面之间高,射入的 X 射线的散射概率也更高。相邻两个平面之间的距离表示为 d d dd ,X 射线的波长表示为 λ λ lambda\lambda ,入射照射角度表示为 θ θ theta\theta 。图 3.4 展示了这一切。
We see from the figure that the two rays have different path lengths; the one penetrating deeper into the crystal travels farther. This path difference means that the rays will experience a phase shift; they are in-phase as they enter the crystal, but not necessarily as they exit. The figure shows that the lower ray travel a total of 2 l 2 l 2l2 l farther than the upper ray. With simple trigonometry, we find that
从图中我们可以看到,两束光线的路径长度不同;穿透晶体更深的那束光线传播得更远。这种路径差异意味着光线会发生相位偏移;它们在进入晶体时是同相位的,但在射出晶体时却不一定。从图中我们可以看出,较低的射线比较高的射线总共传播了 2 l 2 l 2l2 l 远的距离。通过简单的三角计算,我们可以发现

Figure 3.3. Illustration of how constructive and destructive interference occurs from different scattering points. Figure taken from Fundamentals of Powder Diffraction and Structural Characterization of Materials, 2nd ed., by V. K. Pecharsky and P. Y. Zavalij, 2009, New York, USA: Springer. Copyright 2009 by Springer Science+Business Media. Adapted with kind permission from Springer Science+Business Media.
图 3.3.说明不同散射点如何产生建设性和破坏性干涉。图摘自《粉末衍射与材料结构表征基础》,第 2 版,作者 V. K. Pecharsky 和 P. Y. Zavalij,2009 年,美国纽约:施普林格出版社。版权归 Springer Science+Business Media 2009 所有。经 Springer Science+Business Media 许可改编。

Figure 3.4. Simple sketch of two adjacent atomic planes of high electron density. Two parellel and in-phase X-rays enter the crystal and are scattered in the same angle at different depths inside the crystal. When Bragg’s law is fulfilled, the rays will exit the crystal in-phase and interfere constructively.
图 3.4.两个相邻高电子密度原子面的简单草图。两束平行同相的 X 射线进入晶体,并在晶体内部不同深度以相同角度散射。当布拉格定律得到满足时,这两束射线将以同相的方式离开晶体,并发生建设性干涉。
2 l = 2 d sin θ 2 l = 2 d sin θ 2l=2d sin theta2 l=2 d \sin \theta
Bragg’s law is found by seeing that full constructive interference occurs when the path difference equals integer multiples of the wavelength, or in mathematical terms,
布拉格定律的原理是,当路径差等于波长的整数倍时,或用数学术语来说,就会发生完全的建设性干涉、
n λ = 2 d sin θ n λ = 2 d sin θ n lambda=2d sin thetan \lambda=2 d \sin \theta
where n Z + n Z + n inZ^(+)n \in \mathbb{Z}^{+}(also called the order of reflection). In essence, we control the wavelength, vary the angle, measure the reflected intensity, and deduce the unit cell parameters. The intensity is plotted against the diffraction angle 2 θ 2 θ 2theta2 \theta, and the resulting graph is called the “diffractogram”.
其中 n Z + n Z + n inZ^(+)n \in \mathbb{Z}^{+} (也称为反射阶)。实质上,我们控制波长,改变角度,测量反射强度,并推导出单胞参数。强度与衍射角 2 θ 2 θ 2theta2 \theta 相对应,得到的图形称为 "衍射图"。
In the case of powder diffraction, the result is slightly different. A powder basically consists of a vast number of tiny single-crystals, ordered in random orientations. The diffracted wave-pattern is not a symmetrical array of dots, as from a single crystal, but rather a cone with its apex in the origin, and with a cone angle of 4 θ 4 θ 4theta4 \theta. As the incoming waves’ angle is varied, concentric diffraction cones with different cone angles are formed. This is nicely illustrated in Figure 3.5. When placing a detector or a photographic plate behind the powder, these cones will form dark, concentric circles or ellipses on the detection medium with varying intensities, depending on how much constructive interference occured at the specific angle, illustrated in Figure 3.6. These rings, called “Debye rings” (from the Dutch physicist and chemist Peter Debye), are central to the powder diffractogram, and its detection will be described later.
粉末衍射的结果则略有不同。粉末基本上由大量微小的单晶体组成,它们以随机的方向排列。衍射波的图案并不像单晶那样是对称的点阵列,而是一个顶点位于原点的圆锥体,圆锥角为 4 θ 4 θ 4theta4 \theta 。随着入射波角度的变化,会形成不同锥角的同心衍射锥。图 3.5 很好地说明了这一点。如图 3.6 所示,当在粉末后面放置一个检测器或照相板时,这些锥体将在检测介质上形成深色的同心圆或椭圆,其强度各不相同,这取决于特定角度下发生的建设性干涉的程度。这些圆环被称为 "Debye 圆环"(源自荷兰物理学家和化学家 Peter Debye),是粉末衍射图的核心,其检测方法将在下文介绍。

3.1.2 Basic anatomy 3.1.2 基本解剖学

Although X-ray powder diffractometry may be carried out in both transmission geometry and reflection geometry, only the reflection geometry will be covered in this chapter. The reflection geometry is commonly referred to as the “Bragg-Brentano” geometry, named after the physicists Bragg and J. C. M. Brentano.
虽然 X 射线粉末衍射测量可在透射几何和反射几何中进行,但本章只介绍反射几何。反射几何通常被称为 "布拉格-布伦塔诺 "几何,以物理学家布拉格和 J. C. M. 布伦塔诺的名字命名。

Figure 3.5. Illustration of diffraction cones from powder diffraction. Figure taken from Fundamentals of Powder Diffraction and Structural Characterization of Materials, 2nd ed., by V. K. Pecharsky and P. Y. Zavalij, 2009, New York, USA: Springer. Copyright 2009 by Springer Science+Business Media. Adapted with kind permission from Springer Science+Business Media.
图 3.5.粉末衍射的衍射锥示意图。图摘自《粉末衍射与材料结构表征基础》,第 2 版,作者 V. K. Pecharsky 和 P. Y. Zavalij,2009 年,美国纽约:施普林格出版社。版权归 Springer Science+Business Media 2009 所有。经 Springer Science+Business Media 许可改编。

3.1.2.1 The X-ray source 3.1.2.1 X 射线源

X-rays are generated with two main types of devices: X-ray tubes and synchrotrons. Synchrotrons consist of circular tubes (hundreds of meters in diameter) in which charged particles (electrons, protons, etc.) travel. Their stable trajecetory is ensured by magnetic lenses placed on the tube walls. When charged particles accelerate (bend) they emit radiation, which can be varied by varying the particle speed. Synchrotrons are large and expensive to build and maintain, but offer superior quality X-rays compared to X-ray tubes. X-ray tubes, however, are inexpensive and small, fitting in benchtop instruments. Therefore, this section focuses on the typical X-ray tube only.
X 射线主要由两类设备产生:X 射线管和同步加速器。同步加速器由圆管(直径数百米)组成,带电粒子(电子、质子等)在其中穿行。管壁上的磁透镜保证了粒子的稳定运行。当带电粒子加速(弯曲)时,它们会发出辐射,而辐射可以通过改变粒子的速度来改变。同步加速器体积庞大,建造和维护费用高昂,但与 X 射线管相比,它能提供质量上乘的 X 射线。而 X 射线管价格低廉,体积小,适合台式仪器使用。因此,本节仅重点介绍典型的 X 射线管。
Wilhelm Röntgen discovered X-rays in 1895 when operating a Crookes tube (electrical discharge tube), though he did not know that it was X-rays he had discovered. Electrical discharge tubes may emit X-rays when the applied voltage is high enough, resulting in high-energy electrons that lead to fluorescence when colliding with components inside the tube. New kinds of tubes were designed specifically to generate these mysterious X-rays, and X-rays were incorporated in conventional medicine even before the nature of X-rays were understood.
威廉-伦琴于 1895 年在操作克鲁克斯管(放电管)时发现了 X 射线,尽管他当时并不知道自己发现的是 X 射线。当施加的电压足够高时,放电管可能会发射 X 射线,从而产生高能电子,这些电子与管内的元件碰撞时会产生荧光。为了产生这些神秘的 X 射线,人们专门设计了新型的电子管,甚至在人们了解 X 射线的本质之前,X 射线就已经被应用到传统医学中。
These X-ray tubes have not changed much over the 100 or so years since they were
这些 X 射线管自问世以来的 100 多年里并没有太大的变化。

Figure 3.6. Illustration of how diffraction cones are projected onto a flat detector surface. The projected image of several diffraction cones is a set of concentric rings, or segments of concentric rings if the plate is not large enough. Figure taken from Fundamentals of Powder Diffraction and Structural Characterization of Materials, 2nd ed., by V. K. Pecharsky and P. Y. Zavalij, 2009, New York, USA: Springer. Copyright 2009 by Springer Science+Business Media. Adapted with kind permission from Springer Science+Business Media.
图 3.6.衍射锥如何投射到平面探测器表面的示意图。多个衍射锥的投影图像为一组同心圆环,如果平板不够大,则为同心圆环的片段。图摘自《粉末衍射和材料结构表征基础》,第 2 版,作者 V. K. Pecharsky 和 P. Y. Zavalij,2009 年,美国纽约:施普林格出版社。版权归 Springer Science+Business Media 2009 所有。经 Springer Science+Business Media 许可改编。

first made, though, of course, they have been modernized. The modern X-ray tube includes a heated cathode, usually wolfram (W), and a water-cooled anode metal. An electric potential is applied, and loose electrons in the W kathode are accelerated down towards the anode. Most of the energy invovled is lost as heat (hence the water cooling), but some energy is used to generate continuous and characteristic X-rays.
当然,它们已经实现了现代化。现代 X 射线管包括一个加热的阴极(通常是钨(W))和一个水冷的阳极金属。施加电势后,钨阴极中的松散电子被加速向阳极移动。大部分能量以热能的形式散失(因此需要水冷),但也有一些能量被用来产生连续的特征 X 射线。
Continuous X-rays are generated by the mechanism called “bremsstrahlung” (German; breaking radiation), which takes place when the high-energy electrons are descelerated as their trajectory is bent when they interact with the atomic nucleus in the anode metal. They may excite electrons one or more times before leaving the anode material, losing energy as they do so. In the context of X-ray diffraction, bremsstrahlung is not of interest, and is considered noise to be minimized. In Figure 3.7, the continuous part is everything but the sharp peaks.
连续 X 射线是通过 "轫致辐射"(德语:bremsstrahlung)这一机制产生的,当高能电子与阳极金属中的原子核相互作用时,其轨迹发生弯曲,从而产生减速。在离开阳极材料之前,它们可能会激发一次或多次电子,并在此过程中损失能量。在 X 射线衍射中,轫致辐射并不引起人们的兴趣,而被视为需要最小化的噪声。在图 3.7 中,除了尖锐的峰值外,其他部分都是连续的。
Characteristic X-rays are generated by another mechanism. The accelerated kathode electrons may collide with bound electrons in the anode material. Because the accelerated electrons’ energy much exceeds that of the bound electrons, anode atoms may become ionized. When the inner electron ( K shell) is ejected, the newly formed vacancy is filled by an electron from a outer shell ( L or M ). When the L or M electron “falls down”, EM radiation is emitted in the X-ray region. The sharp peaks in Figure 3.7 are characteristic radiation resulting from three different electronic transitions. These X-rays are characteristic because every element’s discrete energy levels are characteristic,
特征 X 射线是通过另一种机制产生的。加速的阴极电子可能会与阳极材料中的束缚电子发生碰撞。由于加速电子的能量远远超过束缚电子的能量,阳极原子可能会发生电离。当内层电子(K 壳)被射出时,新形成的空位会被来自外层(L 或 M 壳)的电子填满。当 L 或 M 电子 "坠落 "时,就会在 X 射线区域发出电磁辐射。图 3.7 中的尖锐峰值是由三种不同的电子跃迁产生的特征辐射。这些 X 射线之所以具有特征,是因为每种元素的离散能级都具有特征、

Figure 3.7. Continuous and characteristic radiation resulting from ejection of K-shell electrons, and filling of the vacancy by either L- or M- shell electrons. The continuous background is of no interest in XRD analysis, and is considered noise. K α 1 , 2 K α 1 , 2 Kalpha_(1,2)\mathrm{K} \alpha_{1,2} is most often used in XRD, while K β K β Kbeta\mathrm{K} \beta is filtered out by either using filters of monochromators. Figure taken from Fundamentals of Powder Diffraction and Structural Characterization of Materials, 2nd ed., by V. K. Pecharsky and P. Y. Zavalij, 2009, New York, USA: Springer. Copyright 2009 by Springer Science+Business Media. Adapted with kind permission from Springer Science+Business Media.
图 3.7.K 壳电子射出和 L 壳或 M 壳电子填补空缺产生的连续和特征辐射。连续本底辐射在 XRD 分析中没有意义,被视为噪声。 K α 1 , 2 K α 1 , 2 Kalpha_(1,2)\mathrm{K} \alpha_{1,2} 在 XRD 中最常用,而 K β K β Kbeta\mathrm{K} \beta 则通过单色器滤波器滤除。图摘自《粉末衍射和材料结构表征基础》,第 2 版,作者 V. K. Pecharsky 和 P. Y. Zavalij,2009 年,美国纽约:施普林格出版社。版权归 Springer Science+Business Media 2009 所有。经 Springer Science+Business Media 许可改编。

and it is these X-rays that are interesting in X-ray diffraction analysis.
而这些 X 射线正是 X 射线衍射分析中令人感兴趣的。

Although the characteristic X -rays are characteristic to each element, it is not monochromatic (although much more so than bremsstrahlung) This is because there is a fine-structure of energy levels within the main electron shells ( K , L K , L K,L\mathrm{K}, \mathrm{L}, and M ), meaning that the emitted characteristic X-rays comprise a mix of different characteristic X-rays; electronic transitions within this fine-structure result in non-pure radiation.
尽管特征 X 射线是每种元素的特征,但它并不是单色的(尽管比轫致辐射要单色得多),这是因为在主电子层( K , L K , L K,L\mathrm{K}, \mathrm{L} 和 M)内存在着能级的精细结构,这意味着发射的特征 X 射线由不同特征的 X 射线混合而成;这种精细结构内的电子跃迁会产生非纯辐射。
Each electron in an atom can be assigned a unique “label” by using the four quantum numbers. Depending on the exact quantum state of the electron involved in filling the vacancy, the emitted characteristic X-rays will vary slightly. For instance, the K α 1 K α 1 Kalpha_(1)\mathrm{K} \alpha_{1} line is the result of a transition from 2 p 3 / 2 2 p 3 / 2 2p_(3//2)2 p_{3 / 2} to 1 s . The K α 2 K α 2 Kalpha_(2)\mathrm{K} \alpha_{2} and K β K β Kbeta\mathrm{K} \beta lines result from other transitions. These transitions, leading to a set of emitted characteristic wavelengths, have consequences for the X-ray diffraction analysis, as the Bragg angle is different for different wavelengths. Several ways of “purifying” the X-rays exist, and they will be outlined later.
通过使用四个量子数,原子中的每个电子都可以被赋予一个独特的 "标签"。根据填充空位的电子的确切量子态,发射的特征 X 射线会略有不同。例如, K α 1 K α 1 Kalpha_(1)\mathrm{K} \alpha_{1} 线是从 2 p 3 / 2 2 p 3 / 2 2p_(3//2)2 p_{3 / 2} 过渡到 1 s 的结果,而 K α 2 K α 2 Kalpha_(2)\mathrm{K} \alpha_{2} K β K β Kbeta\mathrm{K} \beta 线则是其他过渡的结果。这些转变产生了一组发射特征波长,对 X 射线衍射分析产生了影响,因为不同波长的布拉格角是不同的。目前有几种 "净化 "X 射线的方法,稍后将对其进行概述。
The X-ray tube is tightly sealed to not let X-rays escape uncontrollably. However, several beryllium ( Be ) windows are placed next to the anode to let X-rays exit the tube at certain directions. Beryllium is used because of its low atomic number, and hence X-rays have a low probability of interating with the relatively tiny electron cloud. When X-rays exit the tube, they enter the focusing mechanism of the diffractometer.
X 射线管密封严实,不会让 X 射线肆意逃逸。不过,阳极旁边有几个铍(Be)窗口,可以让 X 射线从特定方向射出。使用铍是因为它的原子序数较低,因此 X 射线与相对微小的电子云发生相互作用的概率较低。当 X 射线从管中射出时,会进入衍射仪的聚焦装置。

3.1.2.2 The slits 3.1.2.2 狭缝

Slits have an important part in the X-ray diffractometer. The X-rays emerging from the X -ray source diverge in their propagation, which is bad for resolution. The slits collimate the divergent rays; that is, making them approximately parallel. Various types of slits are comonly used in the diffractometer: soller slits, divergence slits, anti-scatter slits, and the receiving slit.
狭缝在 X 射线衍射仪中占有重要地位。从 X 射线源发出的 X 射线在传播过程中会发散,这不利于分辨率的提高。狭缝可将发散的射线准直,即使其近似平行。衍射仪中使用的狭缝有多种类型:索勒狭缝、发散狭缝、反散射狭缝和接收狭缝。
The soller slit are a set of thin, parallel plates of a certain length in the beam path, stacked next to each other with a certain space between each plate (Figure 3.8). The soller slits collimate the beam, resulting in parallel rays instead of divergent rays. Soller slits are used in both the incident beam and the diffracted beam, usually of the same size at both places. The collimation effect can be increased by decreasing the space between the plates, or by increasing the length of the plates. However, this comes at a cost of the diffracted intenstiy.
索勒狭缝是光束路径上的一组具有一定长度的平行薄板,它们相邻堆叠,每块板之间留有一定空间(图 3.8)。索勒狭缝可对光束进行准直,从而产生平行光线而不是发散光线。索勒狭缝既用于入射光束,也用于衍射光束,两处的尺寸通常相同。可以通过减小平板之间的空间或增加平板的长度来提高准直效果。但是,这需要以降低衍射强度为代价。

Figure 3.8. Illustration of how soller slits collimate the X-ray beam. Non-parallel waves are absorbed by the slits, and hence only waves parallel “enough” are let through. Figure taken from Fundamentals of Powder Diffraction and Structural Characterization of Materials (p. xx), 2nd ed., by V. K. Pecharsky and P. Y. Zavalij, 2009, New York, USA: Springer. Copyright 2009 by Springer Science+Business Media. Adapted with kind permission from Springer Science+Business Media.
图 3.8.索勒狭缝如何准直 X 射线光束的说明。不平行的波会被狭缝吸收,因此只有 "足够 "平行的波才能通过。图摘自《粉末衍射和材料结构表征基础》(第 xx 页),第 2 版,作者 V. K. Pecharsky 和 P. Y. Zavalij,2009 年,美国纽约:施普林格出版社。版权归 Springer Science+Business Media 2009 所有。经 Springer Science+Business Media 许可改编。
The divergence slits are placed in the incident beam, and their job is to reduce the divergence of the X-ray beam. They affect both the intensity and resolution, depending on their placement and opening. The divergence slits may be a fixed opening, resulting in a constant volume of irradiation on the sample; however, the irradiated area is not constant, and decreases as the angle 2 θ 2 θ 2theta2 \theta increases. This may lead to poor quality peaks at high bragg angles. To counter this, automatic-opening slits exist. These slits open up as the irradiation angle increases, resulting in a constant irradiated area on the sample. This improves the peak quality at high bragg angles, but the background has an upward slope as 2 θ 2 θ 2theta2 \theta increases. Software makes it possible to mathematically convert the diffractogram from “automatic divergence slit” to “fixed divergence slit”, which levels out the diffracogram. To achieve a better collimation effect, two divergence slits can be placed in sequence, where the second slit further collimates the beam coming from the first slit.
发散狭缝位于入射光束中,其作用是减少 X 射线光束的发散。它们会影响强度和分辨率,具体取决于它们的位置和开口。发散狭缝的开口可能是固定的,从而使样品上的照射体积恒定;但是,照射面积并不是恒定的,而是随着角度 2 θ 2 θ 2theta2 \theta 的增大而减小。这可能会导致在高布拉格角处出现质量较差的峰值。为了解决这个问题,出现了自动打开狭缝。这些狭缝会随着辐照角度的增加而打开,从而在样品上形成恒定的辐照区域。这提高了高布拉格角下的峰值质量,但随着 2 θ 2 θ 2theta2 \theta 的增加,背景会出现上升斜率。通过软件可以将衍射图从 "自动发散狭缝 "转换为 "固定发散狭缝",从而使衍射图更加平整。为了达到更好的准直效果,可以依次放置两个发散狭缝,其中第二个狭缝可以进一步准直来自第一个狭缝的光束。
Anti-scatter slits are placed in the diffracted beam, and their job is to limit the diffracted rays to those solely scattered by the crystal, and exclude those scattered from air, the sample holder, or from something else. A large anti-scatter slit increases the intensity at the cost of resolution, while a small opening does the opposite. The anti-scatter slits may also be of the fixed or automatic type. The automatic anti-scatted slit are usually set to accept the same length as the sample was irradiated with. Hence, the irradiated length and the “observed length” are usually the same.
反散射狭缝位于衍射光束中,其作用是将衍射光线限制在仅由晶体散射的光线范围内,而将空气、样品架或其他物体散射的光线排除在外。大的反散射狭缝会增加强度,但会降低分辨率,而小的开口则相反。反散射狭缝也可分为固定式和自动式。自动反散射狭缝通常设置为接受与样品照射长度相同的长度。因此,辐照长度和 "观测长度 "通常是相同的。
The receiving slit is placed at the X-ray focal point in the diffracted beam (Ermrich et al. 2011), and defines the intensity and resolution of the detected signal. A large receiving slit increases intensity and reduces resolution, and vica versa. The settings are adjusted according to the specific need of the analysis.
接收狭缝位于衍射光束的 X 射线焦点处(Ermrich 等人,2011 年),决定了探测信号的强度和分辨率。接收狭缝越大,强度越高,分辨率越低,反之亦然。设置可根据分析的具体需要进行调整。

3.1.2.3 The monochromator and filter
3.1.2.3 单色仪和滤波器

The monochromator is used to purify the X-ray beam. This involves reducing the intensity of the K α 2 K α 2 Kalpha_(2)\mathrm{K} \alpha_{2} and K β K β Kbeta\mathrm{K} \beta contributions without sacrificing the K α 1 K α 1 Kalpha_(1)\mathrm{K} \alpha_{1} intensity too much. Usually a beta filter or a crystal monochromator is used.
单色仪用于净化 X 射线束。这包括降低 K α 2 K α 2 Kalpha_(2)\mathrm{K} \alpha_{2} K β K β Kbeta\mathrm{K} \beta 的强度,同时又不过多地牺牲 K α 1 K α 1 Kalpha_(1)\mathrm{K} \alpha_{1} 的强度。通常使用贝塔滤波器或晶体单色仪。
The common monochromator is a single crystal, and works by the principle of Bragg’s law. The crystal is irradiated at a certain angle chosen such that, according to Equation (3.2), only a certain wavelength will be diffracted. The angle is chosen to allow K α 1 K α 1 Kalpha_(1)\mathrm{K} \alpha_{1} to be diffracted. The monochromatic X-rays then passes through collimators and slits and reach the sample. This method eliminates the K α 2 K α 2 Kalpha_(2)\mathrm{K} \alpha_{2} and K β K β Kbeta\mathrm{K} \beta contriutions, while keeping the K α 1 K α 1 Kalpha_(1)\mathrm{K} \alpha_{1} intensity intact.
常见的单色仪为单晶体,根据布拉格定律原理工作。根据公式 (3.2),晶体以一定的角度照射,只有特定的波长会发生衍射。角度的选择是为了让 K α 1 K α 1 Kalpha_(1)\mathrm{K} \alpha_{1} 得到衍射。然后,单色 X 射线通过准直器和狭缝到达样品。这种方法可以消除 K α 2 K α 2 Kalpha_(2)\mathrm{K} \alpha_{2} K β K β Kbeta\mathrm{K} \beta 的影响,同时保持 K α 1 K α 1 Kalpha_(1)\mathrm{K} \alpha_{1} 的强度不变。
A monochromator can also be placed in the diffracted beam. This has other benefits, as it will drastically decrease the background signals. For example, sample fluorescence will be almost completely removed, which is significant for cobolt ( Co ), Fe , and Mn containing samples. Diffracted wavelengths from the sample holder will also be eliminated.
还可以在衍射光束中放置单色仪。这样做还有其他好处,可以大大减少背景信号。例如,样品的荧光几乎会被完全消除,这对含有钴(Co)、铁和锰的样品非常重要。来自样品支架的衍射波长也将被消除。
The beta filter is a thin nickel sheet placed in the incident beam. The filter material depends on the the wavelength of the X-rays used, and hence the anode material in the X -ray tube. The filter material is chosen in such a way that the absorption edge of the filter material lies just before the K α 1 , 2 K α 1 , 2 Kalpha_(1,2)\mathrm{K} \alpha_{1,2} peaks of the X -ray source spectrum. In this way, the filter absorbs the K β K β Kbeta\mathrm{K} \beta wavelength while letting K α 1 , 2 K α 1 , 2 Kalpha_(1,2)\mathrm{K} \alpha_{1,2} pass through. For the common Cu-anode, nickel is used as a beta filter. As is seen in Figure 3.9, most of the beta line is absorbed, while most of the alpha lines are let through. The beta filter method is less expensive than using a crystal monochromator, but has the downside of including the K α 2 K α 2 Kalpha_(2)\mathrm{K} \alpha_{2} component. In addition, although most of the beta line is removed, some intensity is still left in the X-ray beam after the filter. The specific applications for the diffractometer dictates which method should be used.
β滤光片是放置在入射光束中的镍薄片。滤光片的材料取决于所用 X 射线的波长,因此也取决于 X 射线管中的阳极材料。选择滤光片材料时,应使滤光片材料的吸收边缘刚好位于 X 射线源光谱的 K α 1 , 2 K α 1 , 2 Kalpha_(1,2)\mathrm{K} \alpha_{1,2} 峰之前。这样,滤波器就能吸收 K β K β Kbeta\mathrm{K} \beta 波长,而让 K α 1 , 2 K α 1 , 2 Kalpha_(1,2)\mathrm{K} \alpha_{1,2} 波长通过。对于常见的铜阳极,镍被用作贝塔滤光片。如图 3.9 所示,大部分贝塔射线被吸收,而大部分阿尔法射线通过。与使用晶体单色仪相比,β 滤光片法的成本较低,但缺点是会产生 K α 2 K α 2 Kalpha_(2)\mathrm{K} \alpha_{2} 分量。此外,虽然大部分贝塔射线被移除,但滤波器后的 X 射线光束中仍会残留一些强度。衍射仪的具体应用决定了应使用哪种方法。

Figure 3.9. Illustration of the principle behind a beta-filter. The absorption edge lies just before the K α 1 , 2 K α 1 , 2 Kalpha_(1,2)\mathrm{K} \alpha_{1,2} components. Figure taken from Fundamentals of Powder Diffraction and Structural Characterization of Materials, 2nd ed., by V. K. Pecharsky and P. Y. Zavalij, 2009, New York, USA: Springer. Copyright 2009 by Springer Science+Business Media. Adapted with kind permission from Springer Science+Business Media.
图 3.9.贝塔滤波器原理示意图。吸收边缘位于 K α 1 , 2 K α 1 , 2 Kalpha_(1,2)\mathrm{K} \alpha_{1,2} 成分之前。图摘自《粉末衍射与材料结构表征基础》,第 2 版,作者 V. K. Pecharsky 和 P. Y. Zavalij,2009 年,美国纽约:施普林格出版社。版权归 Springer Science+Business Media 2009 所有。经 Springer Science+Business Media 许可改编。

3.1.2.4 The detector 3.1.2.4 探测器

The detector’s job is to record the diffracted X-rays and convert them to electrical signals. Depending on the applications, various different types of detectors are available. The three main types are point detectors, linear detectors, and area detectors.
探测器的工作是记录衍射的 X 射线并将其转换为电信号。根据不同的应用,有各种不同类型的探测器可供选择。三种主要类型是点探测器、线性探测器和区域探测器。
The point detectors can measure the diffracted intensity at only one point along the 2 θ 2 θ 2theta2 \theta scan range. Hence, they are quite slow and inexpensive. Common types are the gas-proprtional counter, the scintillator, and the solid-state detector. In the gasproportional counter (which is used in Geiger counters to detect radioactivity) consists of a sealed chamber filled with a gas. A high electrical potential is applied over the chamber. The X-rays enter the chamber and ionize the gas, and the electrons are attracted to the positive anode. The resulting electrical signal is proprtional to the number of absorbed photons.
点探测器只能测量 2 θ 2 θ 2theta2 \theta 扫描范围内一个点的衍射强度。因此,它们的速度相当慢,而且价格低廉。常见的类型有气体比例计数器、闪烁体和固态探测器。气体比例计数器(用于检测放射性的盖革计数器)由一个充满气体的密封腔组成。在腔体上施加高电位。X 射线进入腔室使气体电离,电子被吸引到正阳极上。由此产生的电信号与吸收的光子数量成正比。
The scintillator, on the other hand, consists of a crystal coupled to a photomultiplier tube (PMT). Here, also, a high voltage is applied over the crystal. When the X-rays are absorbed by the crystal, visible light is emitted which enters the PMT. The PMT consists of a sequence of positively charged electrodes, called dynodes, with an increasing positive charge down the sequence of dynodes. Visible-light photon strikes the first dynode, and ejects a number of electrons from the dynode material, as according to the photoelectric effect. The ejected electrons are then attracted to the second dynode, and each electron ejects a certain amount of new electrons. These then continue to the next dynode, and hence a chain reaction start. The final electrical signal is proprtional to the amount of visible-light photons emitted by the crystal, and is hence proprtional to the amounts of X-ray photons absorbed by the crystal.
闪烁体则由晶体和光电倍增管(PMT)组成。在这里,也是在晶体上施加高压。当 X 射线被晶体吸收后,就会发出可见光,进入 PMT。PMT 由一系列带正电荷的电极(称为 dynodes)组成,正电荷随着 dynodes 的排列而增加。根据光电效应,可见光光子击中第一个 dynode,并从 dynode 材料中射出一些电子。喷出的电子随后被吸引到第二个阳极,每个电子喷出一定量的新电子。然后,这些电子继续进入下一个 dynode,从而开始连锁反应。最终的电信号与晶体发射的可见光光子数量成正比,因此也与晶体吸收的 X 射线光子数量成正比。
The solid-state detector uses a semi-conductor crystal, usually a lithium (Li) doped Si or germanium (Ge) crystal, over which a high voltage is applied. The crystal absorbs the X-rays, and electron-hole pairs are formed. Electrons travel toward the positive anode, and the electrical signal measured electrical signal is proprtional to the amount of absorbed photons. Solid-state detector needs to be cooled to around 80 K to reduce background and migration of Li. Energy resolution of solid-state detectors are very good, and monochromators are not necessary to filter out the K β K β K betaK \beta component. Since even the best crystal monochromators reduce the K α 1 , 2 K α 1 , 2 Kalpha_(1,2)\mathrm{K} \alpha_{1,2} intensities with a factor of 2, this energy resolution is a great advantage.
固态探测器使用半导体晶体,通常是掺锂(Li)的硅(Si)或锗(Ge)晶体,在晶体上施加高压。晶体吸收 X 射线,形成电子-空穴对。电子向正阳极移动,测量到的电信号与吸收的光子数量成正比。固态探测器需要冷却到 80 K 左右,以减少背景和锂的迁移。固态探测器的能量分辨率非常高,不需要单色器来滤除 K β K β K betaK \beta 分量。由于即使是最好的晶体单色器也会将 K α 1 , 2 K α 1 , 2 Kalpha_(1,2)\mathrm{K} \alpha_{1,2} 强度降低 2 倍,因此这种能量分辨率是一个很大的优势。
Linear detectors (also called line, 1D of point-sensitive detectors) cover a limited angular range of 2 θ 2 θ 2theta2 \theta. Short-range detectors may cover up to 10 2 θ 10 2 θ 10^(@)2theta10^{\circ} 2 \theta, while long-range detectors may cover as much as 140 2 θ 140 2 θ 140^(@)2theta140^{\circ} 2 \theta. Modern gas-proprtional counters are able to measure the diffraction angle of the diffracted X-rays because of high-speed electronics. The signal follows two wires to the counting electronics, and depending on where on the anode the electrons hit, the time difference between the two wires is enough to deduce the angle. These need regular maintenence due to aging of ionization gas, and have a low linear dynamic range (Ermrich et al. 2011). A newer and better design is called real-time multiple-strip (RTMS) detectors. These operate in similar ways as the solid-state detector. A number of p -doped strips are placed on an n-doped wafer, and an electric potential is applied over each strip. Electron-hole pairs are formed in the strips where the X-rays are absorbed, and the applient potential makes the electrons travel to the positive anode, where the signal is measured. The electron-holes travel along a path of least resistance, and the current over the potentials at each respective strip provides positional information about the diffracted x-rays. Because an angular range is covered, data collection time is greatly reduced. Collection times of hours with point detectors may be reduced to minutes with linear detectors.
线性探测器(也称为线、点敏感探测器的 1D)覆盖的角度范围有限,为 2 θ 2 θ 2theta2 \theta 。短程探测器的覆盖范围可达 10 2 θ 10 2 θ 10^(@)2theta10^{\circ} 2 \theta ,而长程探测器的覆盖范围可达 140 2 θ 140 2 θ 140^(@)2theta140^{\circ} 2 \theta 。由于采用了高速电子设备,现代气体探测计数器能够测量衍射 X 射线的衍射角。信号通过两根导线传输到计数电子装置,根据电子击中阳极的位置,两根导线之间的时间差足以推断出角度。由于电离气体老化,这些仪器需要定期维护,而且线性动态范围较低(Ermrich 等,2011 年)。一种更新更好的设计被称为实时多条(RTMS)探测器。其工作原理与固态探测器类似。在掺杂 n 的晶片上放置许多掺 p 的条带,并在每个条带上施加电势。在吸收 X 射线的条带中形成电子-空穴对,而施加的电势使电子移动到正阳极,在那里测量信号。电子-空穴沿着阻力最小的路径移动,每个条带的电位上的电流提供了衍射 X 射线的位置信息。由于覆盖了一定的角度范围,数据采集时间大大缩短。使用点探测器需要几个小时的采集时间,而使用线性探测器则可缩短至几分钟。
Area detectors are able to measure the diffracted intensity in two dimensions. They detect larger parts of the debye rings, and even complete rings at small bragg angles. Photographic film is an example of an area detector that is no longer commonly in use in routine laboratories, but modern replacements have been developed.
面积探测器能够测量两个维度的衍射强度。它们可以检测到较大部分的去辉环,甚至是小布拉格角的完整去辉环。照相胶片是面积探测器的一个例子,常规实验室已不再普遍使用,但现代的替代品已经开发出来。

3.1.2.5 The autosampler 3.1.2.5 自动取样器

The autosampler, or sample changer, is a mechanism to choose, place, and replace various different samples. This automates the whole process, making sure the diffractometer can analyze five, 10, 20, or more samples without operator intervention. Different mechanisms exist, depending on manufacturer and patented designs.
自动取样器或样品更换器是一种用于选择、放置和更换各种不同样品的装置。它使整个过程自动化,确保衍射仪可以分析 5 个、10 个、20 个或更多的样品,而无需操作员干预。根据制造商和专利设计的不同,有不同的装置。

3.1.2.6 The goniometer 3.1.2.6 动态关节角度计

The goniometer is the heart of the diffractometer. It usually consists of two arms, holding the X-ray source and incident-beam optics, and the detector and diffracted-
测角仪是衍射仪的核心部件。它通常由两个臂组成,分别固定 X 射线源和事件光束光学器件,以及探测器和衍射光束光学器件。

beam optics. One of the arms, or both, may move in a circular way around the center of the goniometer where the sample holder is placed. The diameter of the circle formed by the moving arms is called the goniometer diameter. The smallest angular step the goniometer arms may move accurately is the limit of angular resolution. The larger the goniometer diameter, the greater the angular resolution is; however, the X-rays will diverge more, air-scatter more, and lose intensity. Most goniometer have a radius of 150 mm to 300 mm
光束光学。其中一个臂或两个臂可以围绕放置样品架的测角仪中心做圆周运动。移动臂形成的圆的直径称为测角仪直径。测角臂可精确移动的最小角度步长是角度分辨率的极限。测角仪直径越大,角度分辨率就越高;但是,X 射线的发散会更大,空气散射会更多,强度也会下降。大多数测角仪的半径为 150 毫米至 300 毫米。
The goniometer may be designed in two different modes, depending on which of the arms move around, and whether or not the sample holder move. The two common goniometer settings are known as θ 2 θ θ 2 θ theta-2theta\theta-2 \theta and θ θ θ θ theta-theta\theta-\theta, and are presented in Figure 3.10 In θ 2 θ θ 2 θ theta-2theta\theta-2 \theta, the sample holder angle is synchronized with the movement of the detector; the incident beam is stationary. In the other mode, θ θ θ θ theta-theta\theta-\theta, the sample holder is held horizontal, and both goniometer arm movements are synchronized. The modes get their names from the angles formed, as seen in Figure 3.10.
动态关节角度计可以设计成两种不同的模式,具体取决于哪一臂左右移动,以及样品架是否移动。两种常见的测角仪设置分别为 θ 2 θ θ 2 θ theta-2theta\theta-2 \theta θ θ θ θ theta-theta\theta-\theta ,如图 3.10 所示。在 θ 2 θ θ 2 θ theta-2theta\theta-2 \theta 模式下,样品架的角度与探测器的移动同步;入射光束静止不动。在另一种模式 θ θ θ θ theta-theta\theta-\theta 中,样品架保持水平,两个测角臂同步移动。如图 3.10 所示,这些模式的名称来自所形成的角度。
Figure 3.11 shows an example of a goniometer equipped with the components we have discussed in this section. This diffractometer is in θ θ θ θ theta-theta\theta-\theta mode, and uses two divergence slits in the incident beam, with soller slits in-between. In the diffracted beam we see an anti-scatter slit and a receiving slit, with soller slits in-between. No monochromator or beta filter is seen, but if the detector is of the solid-state type, this may not be necessary due to the excellent energy resolution. R R RR in the figure refers to the goniometer radius, measured from the center of the sample to the start of the detector.
图 3.11 展示了一个配备本节所讨论组件的测角仪示例。这台衍射仪采用 θ θ θ θ theta-theta\theta-\theta 模式,入射光束中有两个发散狭缝,中间是索勒狭缝。在衍射光束中,我们看到一个反散射狭缝和一个接收狭缝,中间是索勒狭缝。没有看到单色器或β滤光器,但如果探测器是固态类型的,由于能量分辨率极高,可能就不需要单色器或β滤光器了。图中的 R R RR 是指测角仪半径,是从样品中心到探测器起点的测量值。

Figure 3.10. The two goniometer modes geometrically shown. Figure taken from Fundamentals of Powder Diffraction and Structural Characterization of Materials, 2nd ed., by V. K. Pecharsky and P. Y. Zavalij, 2009, New York, USA: Springer. Copyright 2009 by Springer Science+Business Media. Adapted with kind permission from Springer Science+Business Media.
图 3.10.两种测角仪模式的几何图形。图摘自《粉末衍射与材料结构表征基础》,第 2 版,作者 V. K. Pecharsky 和 P. Y. Zavalij,2009 年,美国纽约:施普林格出版社。版权归 Springer Science+Business Media 2009 所有。经 Springer Science+Business Media 许可改编。

3.1.3 Sample preparation 3.1.3 样品制备

Proper sample preparation is extremely important to obtain a high-quality diffractogram. The smaller the particle sizes, the more random the crystallite orientations become, hence reducing the effect of preferred orientation and increasing counting statistics. However, if the particle size is too small, the crystallinity becomes weaker
要获得高质量的衍射图,正确的样品制备极为重要。粒度越小,晶体取向越随机,从而减少了优先取向的影响,提高了计数统计量。但是,如果粒度太小,结晶度会变弱

Figure 3.11. Example of goniometer with attached components. R R RR refers to the goniometer radius. Figure taken from Fundamentals of Powder Diffraction and Structural Characterization of Materials, 2nd ed., by V. K. Pecharsky and P. Y. Zavalij, 2009, New York, USA: Springer. Copyright 2009 by Springer Science+Business Media. Adapted with kind permission from Springer Science+Business Media.
图 3.11.带有附加组件的测角仪示例。 R R RR 指的是测角器半径。图摘自《粉末衍射与材料结构表征基础》,第 2 版,作者 V. K. Pecharsky 和 P. Y. Zavalij,2009 年,美国纽约:施普林格出版社。版权归 Springer Science+Business Media 2009 所有。经 Springer Science+Business Media 许可改编。

and resolution is reduced. A solid sample may be grinded by using a mortar and a pestle, but mechanic mills are available too. Mortars and mills should of course be kept as clean as possible to avoid contaminating the sample. Particle sizes should not be too small, as the particles may start to agglomerate, and too much grinding may degrade the crystallinity of the powder. Heat treatment may be able to restore the crystal structure in some cases.
分辨率也会降低。固体样品可以使用研钵和研杵研磨,也可以使用机械研磨机。当然,研钵和研磨机应尽可能保持清洁,以免污染样品。颗粒尺寸不宜过小,因为颗粒可能会开始聚集,而且研磨过度可能会降低粉末的结晶度。在某些情况下,热处理可以恢复晶体结构。
Not just powder samples can be analyzed. During workplace air assessments, aerosols are deposited on filters, which can be put on a filter holder and placed in the instrument. Very little preparation of filter samples is necessary.
不仅可以分析粉末样本。在工作场所空气评估过程中,气溶胶会沉积在过滤器上,这些过滤器可以放在过滤器支架上,然后放入仪器中。过滤器样本只需很少的准备工作。

3.1.4 Data acquisition 3.1.4 数据采集

Data collection means setting up the method and starting the diffractometer. Various different scan modes exist, examples of which are the step scan and the continuous scan. In a step scan, the goniometer arms move a defined step size and measure the diffracted intensity for a defined amount of time. Measurement time is increased by reducing the step size and increasing the integration time per step. The step size determines the resolution of the resulting diffractogram. In a continuous scan, however, the goniometer arms do not stop at each step, but moves continuously at a speed defined by the operator. The resulting diffractogram is visually identical, but the data collection is slightly different. Instead of measuring the intensity at each step, the
数据采集意味着设置方法和启动衍射仪。有多种不同的扫描模式,例如步进扫描和连续扫描。在步进扫描中,测角臂按规定步长移动,并在规定时间内测量衍射强度。通过减小步长和增加每步的积分时间可以延长测量时间。步长决定了衍射图的分辨率。然而,在连续扫描中,测角臂并不是每一步都停止,而是以操作员定义的速度连续移动。这样得到的衍射图在视觉上是相同的,但数据采集略有不同。测角仪不是测量每一步的强度,而是测量每一步的光强。

software calculates the average intensity within the specified step size. For example, if the intensity at 10 2 θ 10 2 θ 10^(@)2theta10^{\circ} 2 \theta is given, then this may be the average intensity at 9.99 9.99 9.99^(@)9.99^{\circ} and 10.01 10.01 10.01^(@)10.01^{\circ}, with a step size of 0.02 0.02 0.02^(@)0.02^{\circ}. In theory, the step scan mode is slightly more accurate, especially if the goniometer is misaligned.
软件计算指定步长范围内的平均强度。例如,如果给出 10 2 θ 10 2 θ 10^(@)2theta10^{\circ} 2 \theta 处的强度,那么这可能就是 9.99 9.99 9.99^(@)9.99^{\circ} 10.01 10.01 10.01^(@)10.01^{\circ} 处的平均强度,步长为 0.02 0.02 0.02^(@)0.02^{\circ} 。从理论上讲,步进扫描模式要稍微精确一些,尤其是在测角器未对准的情况下。
The sample holder can also be set to spin throughout the scan. This reduces the effect of preferred orientation, and increases the counting statistics, because more bragg angles will be measured. Spinning speeds of 0.5 rpm to 1 rpm are common.
样品架也可以设置为在整个扫描过程中旋转。这可以减少优先取向的影响,并增加计数统计,因为将测量更多的布拉格角。常见的旋转速度为 0.5 转/分钟至 1 转/分钟。
Longer scans give higher quality data, because statistical noise is reduced. This may lead to small peaks becoming visible, that would otherwise not be so. Increasing the scan time is an easy way to increase the quality of the diffractogram.
扫描时间越长,数据质量越高,因为统计噪声会降低。这可能会导致原本不可见的小峰值变得可见。延长扫描时间是提高衍射图质量的简便方法。

3.1.5 Phase identification
3.1.5 阶段识别

Environmental samples are rarily pure substances, but will rather contain several different crystalline compounds with different crystal structures, called phases. All of these compounds will contribute to the diffractogram. If the sample contains four different phases, the Bragg peaks of all four phases will be present in the diffractogram (granted all Bragg angles are found, and the intensity of each peak is large enough to be spotted). These peaks may overlap and further complicate the diffractogram. So how can we distinguish between the phases?
环境样品一般都是纯净物,而是含有几种不同晶体结构的晶体化合物,称为相。所有这些化合物都会对衍射图产生影响。如果样品中含有四种不同的相,那么所有四种相的布拉格峰都会出现在衍射图中(前提是找到了所有的布拉格角,并且每个峰的强度足够大,可以被发现)。这些峰可能会重叠,使衍射图更加复杂。那么我们如何区分这些相呢?
When using PANalytical’s own software for phase identification, HighScore Plus, the phase identification process can be described in the following steps: data inspection, background determination/subtraction, K α 2 K α 2 Kalpha_(2)\mathrm{K} \alpha_{2} stripping, smoothing, peak searching, profile fitting, and search & match analysis.
在使用 PANalytical 自己的相鉴定软件 HighScore Plus 时,相鉴定过程可按以下步骤描述:数据检查、背景确定/抽取、 K α 2 K α 2 Kalpha_(2)\mathrm{K} \alpha_{2} 剥离、平滑、峰搜索、剖面拟合以及搜索和匹配分析。

Data inspection 数据检查

Data inspection usually invovles just visually inspecting the diffractogram and assessing its quality or suitedness for further analysis. Factors such as resolution, background, signal-to-noise ratio, comparing various samples, etc., could be considered.
数据检查通常只是目测衍射图,评估其质量或是否适合进一步分析。可考虑的因素包括分辨率、背景、信噪比、各种样品的比较等。

Background determination/subtraction
背景测定/减法

The first step of the phase identification process should be either subtracting the background signals from the diffractogram, or simply determining and adding it to the observed intensity. If this is not done, false peaks present in the background variation may be wrongfully identified as a peak, or a peak may be wrongfully identified as background, during the peak seraching stage. Therefore, the background levels should be accurately determined. The background may be determined automatically by software algorithms, or manually by defining a set of background points along the diffractogram. The latter is more accurate, but takes more time. In clean and simple diffractograms, automatic background determination may be sufficient, but in complex mixtures with a lot of overlapping peaks, the background may need to be determined manually.
相位识别过程的第一步应该是从衍射图中减去本底信号,或者简单地确定本底信号并将其与观测强度相加。如果不这样做,在峰值选取阶段,背景变化中存在的假峰可能会被错误地识别为一个峰值,或者一个峰值可能会被错误地识别为背景。因此,应准确确定本底水平。本底可以通过软件算法自动确定,也可以通过沿衍射图定义一组本底点来手动确定。后者更为精确,但需要更多时间。在干净简单的衍射图中,自动确定背景可能就足够了,但在有大量重叠峰的复杂混合物中,可能需要手动确定背景。
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