Published as part of a Crystal Growth and Design virtual special issue on The Rietveld Refinement Method: Half of a Century Anniversary The first powder diffraction pattern was reported over a century ago.(1) In a typical powder diffraction measurement, the sample consists of microcrystalline powder with a large number of randomly oriented crystallites. All these crystallites simultaneously diffract the incoming beam in all directions, resulting in diffraction cones. The intensity and distribution of the cones are then measured on the 2θ axis of the powder pattern. The collapse of three-dimensional reciprocal space onto one-dimensional data sets leads to a severe reduction of information, caused by an accidental and systematic peak overlap. This is known as the grave “powder problem”. For the first 50 years, the application of powder diffraction in structural analysis of materials was severely limited. In 1969, Hugo Rietveld published the seminal article(2) on what has become known as the Rietveld refinement method. As a result, in the last 50 years, we have witnessed a true revolution in the application of powder diffraction in crystallographic research. We honor this half of a century anniversary with a collection of articles in a virtual special issue that showcase the applications of the Rietveld method in modern chemistry, materials, and structural sciences. This method offers an elegant way to sidestep the problem of peak overlap. The underlying idea relies on modeling a calculated powder neutron diffraction pattern, described by a set of parameters. These parameters include various contributions to the pattern, such as the background, crystal lattice and symmetry, crystal structure, microstructure, instrumental factors, and others. In fact, with modern software, users can include or omit, fix, or refine any parameter, making the method modular. All of these parameters can be simultaneously refined by the least-squares method, until the calculated pattern matches the experimentally collected data. Once a satisfactory match is achieved, the crystal structure is considered refined. Hugo M. Rietveld studied physics at the University of Western Australia in Perth. In 1960, he and Ted Maslen undertook the first single-crystal neutron diffraction study in Australia, on the organic compound p-diphenyl benzene.(3) In the early days of his research career, automation in data collection was not common, Fourier maps were hand-plotted, and data analysis was tedious. During this time, he became familiar with the IBM 1620 computer, which used Fortran II, with punched cards for input and output. This led him to explore the possibilities of automation made available by the introduction of computers. Four years later, in 1964, Rietveld defended his Ph.D. degree, with Dorothy Hodgkin as an examiner. After his Ph.D., he joined the neutron diffraction group of the Reactor Centrum Nederland (now Netherlands Energy Research Foundation ECN). There, he joined the team of Bert Loopstra and Bob van Laar, who were pioneers in the profile refinement methods.(4,5) In the 1960s, working with low symmetry and complex crystal structures was extremely challenging due to severe overlap of diffraction peaks. The solution to this problem was to refine the crystal structure by using not only single Bragg reflection intensities as data but also a group of overlapping diffraction intensities by profile refinements.(4−6) Attempts were made to separate the overlapping peaks by hand-fitting Gaussian profiles using least-squares procedures, with limited success—complicated patterns demanded fitting of multiple parameters. Rietveld embraced the potential of computers in handling large amounts of data and developed the first algorithm for this purpose.(6,7) Executed on an Electrologica X1 computer (with a storage capacity of just 8192 words and a word length of 28 bits), this algorithm allowed for a simultaneous refinement of up to 33 parameters. This was an improvement, but more computing power was necessary to make a difference. With the arrival of the Electrologica X8 (48 000 words and a word length of 27 bit), the program was rewritten (first in Algol and later in Fortran IV). The new version included refinement of the structure and the profile parameters. As a result, the seminal paper “A Profile Refinement Method for Nuclear and Magnetic Structures” was published in 1969.(2) Although the method was shown on neutron powder diffraction data, it was suggested that it can also be applied on X-ray powder diffraction data. Twenty-seven copies of this program were distributed to research centers all over the world.(8) And history was made. So far, this seminal paper(2) has been cited over 18 000 times. Rietveld originally named the method “Profile Refinement Method” acknowledging the seminal contributions that came before his efforts. However, many authors started using different terminology in their manuscripts. To prevent further naming confusion, during the Neutron conference in Cracow, Terry Sabine and Ray Young proposed the name “Rietveld Method”, which was then accepted by the Commission on Neutron Diffraction.(8) Within 8 years, 172 structures were refined from neutron powder diffraction data. Today, there are thousands. In this virtual special issue, we present a collection of 17 papers that were made possible through the use of the “Rietveld refinement method”. Half a century ago, the powder diffraction method was limited to the refinement of very simple crystal structures of inorganic salts and small organic molecules. To show how much progress has been made, we start this virtual special issue with a staggering increase in complexity—crystal structures of proteins. Margiolaki et al. summarized the beginnings, progress, and possibilities of the Rietveld refinement method in macromolecular powder diffraction (10.1021/acs.cgd.0c00939). Such colossal undertakings in structure refinements would not be possible without key developments and integrations of diffraction line profiles in the Rietveld method, as summarized by Scardi (10.1021/acs.cgd.0c00956). The solution and refinement of complicated and complex crystal structures demand synergetic use of multiple techniques, led by the Rietveld method. In this issue, Kaduk et al. thoroughly analyzed the crystal structure of linagliptin hemihydrate hemiethanolate, using Rietveld refinement, 3D electron diffraction, and density functional theory optimization (10.1021/acs.cgd.0c01379). Harris et al. have shown that structure determination and refinement of multicomponent organic crystalline phases from powder diffraction data can be augmented by complementary experimental and computational techniques (10.1021/acs.cgd.1c00160). Ramos-Guivar et al. have shown the complementary use of the Rietveld method with spectroscopic research, such as μ-Raman, XPS, and Mössbauer spectroscopies (10.1021/acs.cgd.0c01551). Mechanochemistry provides crystalline materials that, sometimes, cannot be obtained by traditional, solvatothermal methods; due to the nature of the method, the mechanochemical reactions usually lead to powders. As shown by Runčevski et al. Rietveld refinement is the remaining alternative to detail the crystal structure of such materials (10.1021/acs.cgd.0c01560). Perfect crystals exist only in theory; in nature, defects and disorder decorate the idealized crystal lattice. Rietveld refinement can help better understand these deviations of the perfect order, as elegantly shown by Chan et al. on defective samples of Yb_0.5Co₃Ge₃ (10.1021/acs.cgd.0c00865). Rabuffetti et al. have shown the rotational disorder in Scheelite-type solids (10.1021/acs.cgd.0c00225). The Rietveld method has made significant contributions in the studies of porous crystalline materials. In this issue, Bon and Kaskel et al. followed the structural evolution of a highly porous responsive metal–organic framework (DUT-49(M)) upon guest desorption by time-resolved powder X-ray diffraction (10.1021/acs.cgd.0c01080). Paillaud et al. report on the investigation on organic structure-directing agent’s locations inside pores of zeolites (10.1021/acs.cgd.1c00322). Various structural properties can be studied by this method. Bette and Dinnebier et al. have applied the Rietveld method in the studies of the crystal structure, polymorphism, and anisotropic thermal expansion of α-Ca(CH₃COO)₂ (10.1021/acs.cgd.0c00563). In situ powder diffraction, coupled with Rietveld refinement, was proven to be an excellent method for following phase transitions, as shown by Dey and Ghosal et al. on agomelatine–phosphoric acid molecular complexes (10.1021/acs.cgd.0c00752). Phase transitions were also studied by Samal et al., who worked on the effect of Bi substitution on the phase transitions of crystals of Cs₃Sb₂Cl₉ (10.1021/acs.cgd.0c00171). Finally, several papers reported on new functional materials investigated by the Rietveld method. Altomare presented a thorough and comprehensive study of the dielectric materials Ca₉Tb(PO₄)₇ and Ca₉Ho(PO₄)₇ (10.1021/acs.cgd.0c01683). Sahu and Kar studied nanostructured zinc oxide for applications in photocatalysis (10.1021/acs.cgd.0c01202). Iwase and Mori reported on the crystal structure, microhardness, and toughness of the important biomineral CaCO₃ (10.1021/acs.cgd.9b01720). Horcajada et al. presented an in-depth structural study on high energy density materials and organic semiconductors (10.1021/acs.cgd.0c00698). We thank all the authors for sharing their excellent contributions to this virtual special issue. We are convinced that over the next 50 years, the Rietveld refinement will remain a cornerstone method in crystallographic studies and will provide the basis for understanding materials functions and applications. This article references 8 other publications.

中文翻译：

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Rietveld 细化方法：半个世纪纪念日

作为晶体生长和设计虚拟特刊的一部分发表在 Rietveld 细化方法：半个世纪周年 一个多世纪前报道了第一个粉末衍射图。(1) 在典型的粉末衍射测量中，样品由微晶组成具有大量随机取向微晶的粉末。所有这些微晶同时在所有方向上衍射入射光束，从而产生衍射锥。然后在粉末图案的 2θ 轴上测量锥体的强度和分布。三维倒易空间坍塌到一维数据集会导致信息严重减少，这是由偶然和系统的峰值重叠引起的。这被称为严重的“粉末问题”。在最初的 50 年里，粉末衍射在材料结构分析中的应用受到严重限制。1969 年，Hugo Rietveld 发表了关于 Rietveld 细化方法的开创性文章 (2)。因此，在过去的 50 年中，我们见证了粉末衍射在晶体学研究中的应用发生了真正的革命。我们通过虚拟特刊中的一系列文章来纪念这半个世纪的周年纪念，这些文章展示了 Rietveld 方法在现代化学、材料和结构科学中的应用。这种方法提供了一种避免峰重叠问题的优雅方法。基本思想依赖于对计算出的粉末中子衍射图进行建模，该图由一组参数描述。这些参数包括对图案的各种贡献，例如背景、晶格和对称性、晶体结构、微观结构、仪器因素等。事实上，使用现代软件，用户可以包括或省略、修复或改进任何参数，使方法模块化。所有这些参数都可以通过最小二乘法同时细化，直到计算出的模式与实验收集的数据相匹配。一旦达到令人满意的匹配，晶体结构就被认为是精细的。Hugo M. Rietveld 在珀斯的西澳大利亚大学学习物理学。1960年，他和Ted Maslen在澳大利亚进行了第一次单晶中子衍射研究，对有机化合物 使方法模块化。所有这些参数都可以通过最小二乘法同时细化，直到计算出的模式与实验收集的数据相匹配。一旦达到令人满意的匹配，晶体结构就被认为是精细的。Hugo M. Rietveld 在珀斯的西澳大利亚大学学习物理学。1960年，他和Ted Maslen在澳大利亚进行了第一次单晶中子衍射研究，对有机化合物 使方法模块化。所有这些参数都可以通过最小二乘法同时细化，直到计算出的模式与实验收集的数据相匹配。一旦达到令人满意的匹配，晶体结构就被认为是精细的。Hugo M. Rietveld 在珀斯的西澳大利亚大学学习物理学。1960年，他和Ted Maslen在澳大利亚进行了第一次单晶中子衍射研究，对有机化合物磷-二苯基苯。(3) 在他研究生涯的早期，数据收集的自动化并不常见，傅立叶图是手工绘制的，数据分析很乏味。在此期间，他熟悉了 IBM 1620 计算机，该计算机使用 Fortran II，具有用于输入和输出的穿孔卡片。这促使他探索通过引入计算机实现自动化的可能性。四年后，也就是 1964 年，里特维尔德 (Rietveld) 为他的博士学位辩护。学位，多萝西·霍奇金担任考官。博士毕业后加入Reactor Centrum Nederland（现荷兰能源研究基金会ECN）的中子衍射组。在那里，他加入了轮廓细化方法的先驱 Bert Loopstra 和 Bob van Laar 的团队。(4,5) 在 1960 年代，由于衍射峰的严重重叠，处理低对称性和复杂的晶体结构极具挑战性。解决这个问题的方法是通过不仅使用单个布拉格反射强度作为数据，而且通过轮廓细化使用一组重叠的衍射强度来细化晶体结构。 (4-6) 尝试通过手工拟合分离重叠峰使用最小二乘法的高斯分布，成功率有限——复杂的模式需要拟合多个参数。Rietveld 充分利用了计算机处理大量数据的潜力，并为此开发了第一个算法。 (6,7) 在 Electrologica X1 计算机上执行（存储容量仅为 8192 字，字长为 28 位），该算法允许同时优化多达 33 个参数。这是一种改进，但需要更多的计算能力才能有所作为。随着 Electrologica X8（48 000 字和 27 位字长）的到来，程序被重写（首先在 Algol 中，后来在 Fortran IV 中）。新版本包括对结构和轮廓参数的改进。结果，1969 年发表了开创性论文“A Profile Refinement Method for Nuclear and Magnetic Structures”。 (2) 虽然该方法显示在中子粉末衍射数据上，但有人建议它也可以应用于 X 射线粉末衍射数据。这个程序的 27 个副本被分发到世界各地的研究中心。(8) 创造了历史。迄今为止，这篇开创性论文(2) 已被引用超过18 000 次。Rietveld 最初将该方法命名为“Profile Refinement Method”，以承认在他的努力之前做出的开创性贡献。然而，许多作者开始在他们的手稿中使用不同的术语。为了防止进一步的命名混乱，在克拉科夫的中子会议期间，Terry Sabine 和 Ray Young 提出了“Rietveld 方法”的名称，随后被中子衍射委员会接受。(8) 在 8 年内，从中子中提炼出 172 个结构粉末衍射数据。今天，有数千人。在这个虚拟的特刊中，我们展示了 17 篇论文的集合，这些论文是通过使用“Rietveld 细化方法”实现的。半个世纪前，粉末衍射方法仅限于对无机盐和有机小分子的非常简单的晶体结构进行细化。为了展示已经取得了多大的进展，我们从复杂性的惊人增加开始这个虚拟的特刊——蛋白质的晶体结构。马乔拉基等人。总结了大分子粉末衍射中 Rietveld 精修方法的开始、进展和可能性 (10.1021/acs.cgd.0c00939)。如斯卡迪 (10.1021/acs.cgd.0c00956) 所总结的，如果没有 Rietveld 方法中衍射线轮廓的关键发展和整合，结构改进方面的这种巨大努力是不可能的。复杂和复杂晶体结构的求解和改进需要以 Rietveld 方法为主导的多种技术的协同使用。在这个问题上，Kaduk 等人。使用 Rietveld 精修、3D 电子衍射彻底分析了利格列汀半水合物半乙醇化物的晶体结构，和密度泛函理论优化 (10.1021/acs.cgd.0c01379)。哈里斯等人。已经表明，可以通过互补的实验和计算技术（10.1021/acs.cgd.1c00160）增强粉末衍射数据中多组分有机结晶相的结构确定和细化。拉莫斯-吉瓦尔等人。已经展示了 Rietveld 方法与光谱研究的互补使用，例如 μ-拉曼、XPS 和穆斯堡尔光谱 (10.1021/acs.cgd.0c01551)。机械化学提供的结晶材料有时无法通过传统的溶剂热方法获得；由于该方法的性质，机械化学反应通常会产生粉末。正如 Runčevski 等人所示。Rietveld 细化是详细描述此类材料晶体结构的剩余替代方法 (10.1021/acs.cgd. 0c01560）。完美的晶体只存在于理论上；在自然界中，缺陷和无序装饰着理想化的晶格。正如 Chan 等人优雅地展示的那样，Rietveld 细化可以帮助更好地理解完美顺序的这些偏差。关于 Yb 的缺陷样品_0.5 Co ₃ Ge ₃(10.1021/acs.cgd.0c00865)。拉布菲蒂等。已经显示出白钨矿型固体的旋转无序 (10.1021/acs.cgd.0c00225)。Rietveld 方法在多孔晶体材料的研究中做出了重大贡献。在这个问题上，Bon 和 Kaskel 等人。通过时间分辨粉末 X 射线衍射 (10.1021/acs.cgd.0c01080) 在客体解吸时跟踪高度多孔响应金属-有机骨架 (DUT-49(M)) 的结构演变。帕约德等人。关于沸石孔内有机结构导向剂位置的调查报告（10.1021/acs.cgd.1c00322）。通过这种方法可以研究各种结构特性。Bette 和 Dinnebier 等人。已将 Rietveld 方法应用于 α-Ca(CH ₃首席运营官) ₂ (10.1021/acs.cgd.0c00563)。如 Dey 和 Ghosal 等人所示，原位粉末衍射与 Rietveld 精修相结合，被证明是跟踪相变的极好方法。关于阿戈美拉汀-磷酸分子复合物 (10.1021/acs.cgd.0c00752)。Samal 等人也研究了相变，他们研究了 Bi 取代对 Cs ₃ Sb ₂ Cl ₉晶体相变的影响(10.1021/acs.cgd.0c00171)。最后，几篇论文报道了通过 Rietveld 方法研究的新功能材料。Altomare 对介电材料 Ca ₉ Tb(PO ₄ ) _{7 进行}了彻底而全面的研究和 Ca ₉ Ho(PO ₄ ) ₇ (10.1021/acs.cgd.0c01683)。Sahu 和 Kar 研究了用于光催化应用的纳米结构氧化锌 (10.1021/acs.cgd.0c01202)。Iwase 和 Mori 报告了重要的生物矿物 CaCO ₃的晶体结构、显微硬度和韧性(10.1021/acs.cgd.9b01720)。霍卡哈达等人。介绍了对高能量密度材料和有机半导体的深入结构研究 (10.1021/acs.cgd.0c00698)。我们感谢所有作者分享他们对这个虚拟特刊的出色贡献。我们相信，在接下来的 50 年里，Rietveld 精修仍将是晶体学研究的基石方法，并将为理解材料功能和应用提供基础。本文引用了 8 篇其他出版物。