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Opportunities and challenges in understanding complex functional materials
理解复杂功能材料的机遇与挑战

Andrew L. Goodwin © 1 ⋆ 1 ⋆ ^(1***){ }^{1 \star}
安德鲁·L·古德温 © 1 ⋆ 1 ⋆ ^(1***){ }^{1 \star}

Understanding complex functional materials suffers from needing to capture structural features on many length scales. By quantitatively combining complementary experimental measurements, realistic models can now be generated. Here, I discuss the strengths and limits of this approach, but also advocate focusing on the interactions that drive structural complexity instead.
理解复杂功能材料面临的核心挑战在于需要捕捉多尺度结构特征。如今通过定量整合互补性实验测量数据，已能构建真实可信的模型。本文在探讨该方法优势与局限的同时，更主张聚焦驱动结构复杂性的相互作用机制本身。

Complexity in functional materials
功能材料的复杂性

The extent to which a material’s structure is simple or complex reflects the amount of information required to describe it. The structure of silicon, for example, is simple because it is captured entirely by a handful of structural parameters. Crystallographic symmetry is clearly crucial, because it projects the enormous number of degrees of freedom in the bulk onto extremely few microscopic descriptors. By contrast, relaxor ferroelectrics are complex because their compositions and structures vary over the nanometre length scale, and so any realistic model must contain the positions of many hundreds of thousands of atoms 1 1 ^(1){ }^{1}. For relaxors, this complexity is considered responsible for their unusual dielectric properties. No model of a complex material is ever unique: different regions of the system will correspond to different individual sets of atomic coordinates. The best one can do is to make a model sufficiently large (and realistic) to capture all key features and correlations, and hence be representative of the whole.
材料结构的简单或复杂程度反映了描述它所需的信息量。以硅为例，其结构简单，因为仅需少量结构参数即可完整描述。晶体学对称性显然至关重要，因为它将材料内部庞大的自由度投射到极少数微观描述符上。相比之下，弛豫铁电体结构复杂，因为其成分和结构在纳米尺度上就会发生变化，因此任何真实模型都必须包含数十万个原子的位置 1 1 ^(1){ }^{1} 。对于弛豫铁电体，这种复杂性被认为是其特殊介电性能的根源。复杂材料的模型永远不具备唯一性：系统的不同区域会对应不同的原子坐标组合。我们所能做的最佳方案是建立足够大（且真实）的模型，以捕捉所有关键特征与关联性，从而具有整体代表性。
Unsurprisingly, the atomic-scale structures of complex materials are difficult to determine. Crystallographic approaches are sensitive to anything periodic; i.e., the ‘average structure’. Local probes provide information about deviations away from this average, but different tools capture different many-body correlations, and so are sensitive to local structure in different ways. However expertly carried out, each individual measurement nonetheless provides an incomplete picture of the true structure. If understanding the function of complex materials truly depends on determining their atomic-scale structures, then the clear challenge is to develop and apply a self-consistent methodology for pulling together these various complementary measurements. This is the long-recognised objective of so-called complex modelling 2 2 ^(2){ }^{2}. There is also the possibility, however, that the underlying physics of complex functional materials might be captured much more simply by focusing on interactions rather than structure.
毫不意外，复杂材料的原子尺度结构难以测定。晶体学方法对任何周期性特征（即"平均结构"）极为敏感。局域探针能获取偏离该平均结构的畸变信息，但不同检测工具捕捉到的多体关联性各异，因而对局域结构的敏感方式也各不相同。即便操作再专业，单项测量仍无法完整呈现真实结构全貌。若理解复杂材料功能确实依赖于测定其原子尺度结构，那么核心挑战就在于开发并应用一套自洽方法论，将这些互补性测量结果有机整合——这正是所谓"复杂建模" 2 2 ^(2){ }^{2} 长期公认的目标。然而另一种可能是：聚焦相互作用而非结构本身，或许能更简洁地捕捉复杂功能材料的底层物理机制。

Hierarchical structure of a relaxor ferroelectric
弛豫铁电体的多级结构

Probably the most successful and thorough application of complex modelling to date is a recent study of the canonical (and ever controversial) relaxor ferroelectric PbMg 1 / 3 Nb 2 / 3 O 3 ( PMN ) 3 PbMg 1 / 3 Nb 2 / 3 O 3 ( PMN ) 3 PbMg_(1//3)Nb_(2//3)O_(3)(PMN)^(3)\mathrm{PbMg}_{1 / 3} \mathrm{Nb}_{2 / 3} \mathrm{O}_{3}(\mathrm{PMN})^{3}.
迄今为止，复杂建模最为成功且全面的应用案例当属近期对典型（且争议不断）弛豫铁电体 PbMg 1 / 3 Nb 2 / 3 O 3 ( PMN ) 3 PbMg 1 / 3 Nb 2 / 3 O 3 ( PMN ) 3 PbMg_(1//3)Nb_(2//3)O_(3)(PMN)^(3)\mathrm{PbMg}_{1 / 3} \mathrm{Nb}_{2 / 3} \mathrm{O}_{3}(\mathrm{PMN})^{3} 的研究。
As for many complex materials, the average structure of PMN is described by a deceptively simple, high-symmetry unit cell. Yet its technologically relevant response to electric fields arises from deviations away from this high-symmetry structure, in the form of compositional variation and large-scale cation off-centering. The extent to which off-centre displacements are coupled to the non-random distribution of Nb 5 + Nb 5 + Nb^(5+)\mathrm{Nb}^{5+} and Mg 2 + Mg 2 + Mg^(2+)\mathrm{Mg}^{2+} ions, and the nature of structural inhomogeneities on the nanometre scale are both long-standing open questions.
与众多复杂材料类似，PMN 的平均结构由一个看似简单的高对称性晶胞描述。然而，其对电场响应的技术相关性实则源于对这种高对称结构的偏离——表现为成分变化和大尺度阳离子偏心现象。阳离子偏心位移与 Nb 5 + Nb 5 + Nb^(5+)\mathrm{Nb}^{5+} 和 Mg 2 + Mg 2 + Mg^(2+)\mathrm{Mg}^{2+} 离子非随机分布的耦合程度，以及纳米尺度结构不均匀性的本质，这两个问题长期以来悬而未决。
The real success of ref. 3 3 ^(3){ }^{3} was to combine the complementary structural information contained within eight distinct experimental data sets-spanning neutron and X-ray scattering, diffraction and element-specific X-ray absorption measurements, real- and reciprocal-space normalisations, for both powder and single-crystal samples-to arrive at a single consistent structural model of PMN. For context, most previous complex modelling studies-whether of PMN or of entirely separate systems-have included at most two or three data sets. The step-change here was made possible by a recent optimised implementation of the complex modelling code rmcProfile 4 4 ^(4){ }^{4}, which used the reverse Monte Carlo (RMC) algorithm to construct of a 320,000 -atom representation of the PMN structure consistent with the entire ensemble of input data. The hierarchical nature of the PMN structure is illustrated and described in Fig. 1a-d.
参考文献 3 3 ^(3){ }^{3} 的真正成功之处在于整合了八组不同实验数据集中互补的结构信息——涵盖中子和 X 射线散射、衍射及元素特异性 X 射线吸收测量，实空间与倒易空间归一化处理，同时包含粉末和单晶样品数据——最终得出了 PMN 的单一自洽结构模型。作为对比，以往大多数复杂建模研究（无论是针对 PMN 还是其他体系）最多仅包含两到三组数据集。这一突破性进展得益于复杂建模代码 rmcProfile 4 4 ^(4){ }^{4} 的最新优化实现，该代码采用逆向蒙特卡洛（RMC）算法构建了与所有输入数据相吻合的 32 万原子级 PMN 结构表征。图 1a-d 展示并阐释了 PMN 结构的多层级特征。

Making realistic models of complex materials
构建复杂材料的真实模型

At face value, we now find ourselves with a powerful-if computationally and experimentally demanding-tool capable of determining the structures of materials of perhaps arbitrary complexity. If this approach proves robust, it could provide unparalleled insight into the microscopic nature of all sorts of
乍看之下，我们现在拥有了一种强大的工具——尽管在计算和实验层面要求极高——能够解析可能具有任意复杂性的材料结构。若该方法被证实具有稳健性，它将为各类复杂系统的微观本质提供前所未有的洞见：例如电池材料、生物矿物、光伏材料、热电材料和多相催化剂等典型体系。
complex systems: examples include battery materials, biominerals, photovoltaics, thermoelectrics and heterogeneous catalysts. As systems become trickier and trickier to characterise, we might simply add to our modelling algorithm more and more data sets of increasing quality and increasingly diverse sensitivity. Even for the case of PMN, one might eventually wish to include small-angle scattering, threedimensional pair distribution function (3D-PDF) and/or spectroscopic measurements.
随着待表征体系变得越来越复杂，我们或许只需在建模算法中持续加入质量更高、敏感度更趋多元化的数据集。即便对于 PMN（铌镁酸铅）这类材料，研究者最终也可能希望引入小角散射、三维原子对分布函数（3D-PDF）和/或光谱测量等数据。
A key difficulty is always going to be that of knowing how much to trust the answer. I do not think it’s yet clear, for example, how large is the error bar on the hierarchical structure of PMN. Even if experimental uncertainties were propagated fully-and there are good reasons why it is difficult to do so for e.g., PDF measurements-determining the uncertainty in emergent features is an even greater and less well-defined challenge. Checking for consistency in independent instances of a complex modelling process is of course good practice. Yet consistency is a necessary-but-not-sufficient criterion for correct structure solution: stochastic methods such as RMC are biased towards configurationally accessible solutions, whether or not they are actually physical 5 5 ^(5){ }^{5}. Deterministic alternatives, such as the Diffpy-CMI approach 6 6 ^(6){ }^{6}, are also not immune from uniqueness problems, and suffer more generally from the need to identify ab initio a suitable nanostructure model. In particular, one never knows whether a more physical model may exist and account for the same experimental observables equally well (or indeed more accurately 7 7 ^(7){ }^{7} ).
一个关键难点始终在于如何判断对结果的信任程度。例如，目前尚不明确 PMN 层级结构误差范围的具体大小。即便实验不确定性被完全传递——对于 PDF 测量等技术而言确实存在难以实现的客观原因——确定涌现特征中的不确定性则是更具挑战性且更难以界定的难题。在复杂建模过程中验证多个独立实例的一致性固然是良好实践，但一致性只是获得正确结构解的必要非充分条件：诸如 RMC 之类的随机方法会偏向于构型上可实现的解，无论这些解是否真实符合物理规律 5 5 ^(5){ }^{5} 。而确定性方法如 Diffpy-CMI 6 6 ^(6){ }^{6} 同样无法避免唯一性问题，且更普遍面临需要从头识别合适纳米结构模型的困境。尤其令人困扰的是，我们永远无法确知是否存在更符合物理实际的模型，能够同样好地（甚至更精确地 7 7 ^(7){ }^{7} ）解释相同的实验观测数据。
An obvious means of correcting this bias so as to favour physical solutions is to exploit energy calculations during the modelling process. The conventional approach is to include simple empirical potentials e.g. to constrain bond lengths and
在建模过程中利用能量计算是纠正这种偏向物理解决方案偏见的明显方法。传统做法是引入简单的经验势能，例如用于约束键长和
Primary  初级 Secondary  次级 Tertiary  三级 Quaternary  四元
Microscopic  微观 Local cooperative  局域协同 Emergent collective  涌现集体 Functional  功能性
Degree of freedom  自由度 order  有序性 object  对象 assembly  组装
Primary Secondary Tertiary Quaternary Microscopic Local cooperative Emergent collective Functional Degree of freedom order object assembly| Primary | Secondary | Tertiary | Quaternary | | :---: | :---: | :---: | :---: | | Microscopic | Local cooperative | Emergent collective | Functional | | Degree of freedom | order | object | assembly |
Fig. 1 Hierarchical structures of complex materials. a-d The structure of PbMg 1 / 3 Nb 2 / 3 O 3 PbMg 1 / 3 Nb 2 / 3 O 3 PbMg_(1//3)Nb_(2//3)O_(3)\mathrm{PbMg}_{1 / 3} \mathrm{Nb}_{2 / 3} \mathrm{O}_{3} relaxor ferroelectric determined in ref. 3 3 ^(3){ }^{3}. a At the unit-cell level, the cations are displaced from their high-symmetry positions (arrow) at the centre of the perovskite cages (balls and sticks), and these displacements are correlated with local composition. b b b\mathbf{b} Neighbouring unit cells tend to coalign their displacements, forming domains with a collective polarisation.
图 1 复杂材料的分级结构。a-d 参考文献 3 3 ^(3){ }^{3} 中确定的 PbMg 1 / 3 Nb 2 / 3 O 3 PbMg 1 / 3 Nb 2 / 3 O 3 PbMg_(1//3)Nb_(2//3)O_(3)\mathrm{PbMg}_{1 / 3} \mathrm{Nb}_{2 / 3} \mathrm{O}_{3} 弛豫铁电体结构。a 在晶胞层面，阳离子从其高对称位置（箭头所示）偏离钙钛矿笼中心（球棍模型所示），这些位移与局部成分相关。 b b b\mathbf{b} 相邻晶胞倾向于协同排列其位移，形成具有集体极化的畴。
c Collections of nearly aligned domains form larger structures consistent with the polar nanoregion (PNR) model discussed widely in relaxor ferroelectric literature’. d Finally, the bulk structure consists of a dense packing of these PNRs (here different PNR orientations are shown in different colours, with gradation reflecting the presence of nearly-aligned sub-domains). e − h e − h e-h\mathbf{e}-\mathbf{h} The magnetic structure of a MnSi skyrmion crystal. e e e\mathbf{e} Magnetic moments of Mn atoms (black arrow) on the chiral MnSi lattice couple ferromagnetically to give ( f f f\mathbf{f} ) a net local magnetisation (large red arrow). g g g\mathbf{g} On larger length scales, the underlying lattice chirality causes this magnetisation to twist on itself, giving rise to a knotting of the magnetisation field known as a skyrmion. Here, arrows are coloured according to the orientation of the magnetisation field, and the yellow surface denotes a region of constant magnetisation surrounding the one-dimensional skyrmion core. h h h\mathbf{h} In the bulk, these skyrmions assemble into a crystal phase, which in turn can be observed and manipulated directly. Panel figure adapted from ref. 13 13 ^(13){ }^{13}. Reprinted with permission from AAAS
c 近乎平行排列的畴区集合形成了与弛豫铁电体文献中广泛讨论的极性纳米区域（PNR）模型相吻合的更大结构。d 最终，整体结构由这些 PNR 的密集堆积构成（此处不同颜色的 PNR 取向代表不同方向，颜色渐变反映近取向子畴的存在）。 e − h e − h e-h\mathbf{e}-\mathbf{h} MnSi 斯格明子晶体的磁结构。 e e e\mathbf{e} 手性 MnSi 晶格上 Mn 原子的磁矩（黑色箭头）通过铁磁耦合产生（ f f f\mathbf{f} ）净局部磁化强度（大红箭头）。 g g g\mathbf{g} 在更大尺度上，底层晶格的手性导致磁化方向自身扭转，形成被称为斯格明子的磁化场扭结结构。图中箭头根据磁化场方向着色，黄色表面表示围绕一维斯格明子核心的恒定磁化区域。 h h h\mathbf{h} 在体材料中，这些斯格明子会组装成晶相，该晶相可直接被观测和操控。面板图改编自文献 13 13 ^(13){ }^{13} 。经美国科学促进会许可转载。
angles 4 4 ^(4){ }^{4}, but newer frameworks anticipate the possibility for incorporating calculations based on higher-level theory 8 8 ^(8){ }^{8}. A particularly exciting opportunity is the interface with efficient machine-learned potentials that allow energy calculations with density functional theory accuracy even for large atomistic configurations 9 9 ^(9){ }^{9}. Whatever methodology one might use, the relative likelihood p p pp of any two competing models (A and B, say) is in principle entirely determined by the difference in corresponding (free) energies E : p A / p B = exp ⁡ [ − ( E A − E B ) / k B T ] E : p A / p B = exp ⁡ − E A − E B / k B T E:p_(A)//p_(B)=exp[-(E_(A)-E_(B))//k_(B)T]E: p_{\mathrm{A}} / p_{\mathrm{B}}=\exp \left[-\left(E_{\mathrm{A}}-E_{\mathrm{B}}\right) / k_{\mathrm{B}} T\right]. Bayes’ theorem could then be used to weight experiment and theory (exactly) in the case that experimental uncertainties are properly handled. Given the recent developments in both experiment-driven and computation-driven complex structure solution, we now have the right mise en place for a truly integrated methodology that promises the most realistic structural models possible. Two particular challenges remain: one is the computational difficulty of accounting for the contribution of entropy (doable, but slow), and the second is the trickier problem that complex materials need not be equilibrium phases.
角度 4 4 ^(4){ }^{4} ，但较新的框架预期了融入基于更高阶理论计算的可能性 8 8 ^(8){ }^{8} 。特别令人振奋的机遇在于与高效机器学习势函数的结合，即使对于大型原子构型也能实现密度泛函理论精度的能量计算 9 9 ^(9){ }^{9} 。无论采用何种方法，两种竞争模型（例如 A 与 B）的相对可能性 p p pp 原则上完全由对应（自由）能差值决定 E : p A / p B = exp ⁡ [ − ( E A − E B ) / k B T ] E : p A / p B = exp ⁡ − E A − E B / k B T E:p_(A)//p_(B)=exp[-(E_(A)-E_(B))//k_(B)T]E: p_{\mathrm{A}} / p_{\mathrm{B}}=\exp \left[-\left(E_{\mathrm{A}}-E_{\mathrm{B}}\right) / k_{\mathrm{B}} T\right] 。若实验不确定性得到妥善处理，便可运用贝叶斯定理对实验与理论进行精确加权。鉴于实验驱动与计算驱动的复杂结构解析领域最新进展，我们现在已具备实现真正集成方法的基础条件，有望获得最接近现实的结构模型。仍存在两大挑战：其一是计算熵贡献存在技术难度（可行但耗时），其二则是更棘手的问题——复杂材料未必处于平衡相态。

Recovering simplicity: from structure to interaction
回归简约：从结构到相互作用

Yet all this effort is predicated on one fundamental assumption: that by knowing the structure of a complex material, we will better understand its underlying physics. No doubt this is true, at least in part, for PMN. Its domainlike architecture does indeed help explain the unusual response to external electric fields, even if the physics that drive this particular structure remain opaque. But what if there had been no domains? Interpreting atomistic models for complex materials is its own particular challenge: my personal experience is that it can be very difficult to find the right order parameter to reveal hidden patterns 10 10 ^(10){ }^{10}, and one is never certain that any description is ever complete. Meanwhile, in the parallel field of liquids and amorphous materials, it is increasingly clear that collective measures (such as density or mean-squared displacement) are often a better descriptor of properties than are atomic coordinates 11 11 ^(11){ }^{11}.
然而所有这些努力都基于一个根本假设：通过了解复杂材料的结构，我们将更深入理解其基础物理原理。对于 PMN（铌镁酸铅）而言，这至少在部分程度上是成立的——其类畴结构确实有助于解释对外加电场的异常响应，尽管驱动这种特殊结构的物理机制仍不明确。但如果没有这些电畴存在呢？解读复杂材料的原子模型本身就是个特殊挑战：根据我的个人经验，要找到能揭示隐藏模式的正确序参量极其困难 10 10 ^(10){ }^{10} ，且永远无法确定任何描述是否完整。与此同时，在液体与非晶态材料这一平行研究领域，越来越清晰的共识是：集体性度量指标（如密度或均方位移）往往比原子坐标更能有效表征材料特性 11 11 ^(11){ }^{11} 。
One alternative is to focus on interactions, rather than structure. This is generally the approach of direct modelling, whereby a given interaction model is used to drive (e.g.,) a Monte Carlo or molecular dynamics simulation, which in turn is assessed in terms of its ability to account for experimental observables 12 12 ^(12){ }^{12}. The clear advantage is that the output is the physics itself: namely, how individual components of a system interact so as to produce the various effects observed experimentally.
另一种选择是关注相互作用而非结构。这通常是直接建模的方法，即使用给定的相互作用模型来驱动（例如）蒙特卡洛或分子动力学模拟，然后根据其解释实验观测数据的能力进行评估 12 12 ^(12){ }^{12} 。其明显优势在于输出结果本身就是物理机制：即系统的各个组成部分如何相互作用，从而产生实验中观察到的各种效应。
There is a particular beauty in the finding that complex structures can emerge from simple interactions. Many examples are known, but Fig. 1e-h illustrates the specific case of skyrmion magnets. Here, a handful of ingredients-ferromagnetism, lattice chirality and antisymmetric exchange-give rise to a hierarchical ‘skyrmion crystal’ phase at specific combinations of temperatures and magnetic field 13 13 ^(13){ }^{13}. So this ostensibly complex magnetic structure can be captured much more simply in terms of very few microscopic interactions. The system complexity is reduced fundamentally by shifting from atomic positions to atomic interactions. An obvious question is whether the hierarchical structure of PMN shown in Fig. 1a-d might also emerge from relatively simple interactions. Indeed an interaction-based model for PMN was developed in ref. 14 14 ^(14){ }^{14}, and the immediate community will no doubt wish to compare the results of that study with the recent RMC work. In particular, if it can be shown that both arrive at essentially equivalent real-space descriptions, then the structural complexity evident in Fig. 1a-d arises entirely from a
发现简单相互作用能产生复杂结构这件事蕴含着独特的美感。已知的例证不胜枚举，而图 1e-h 展示的斯格明子磁体便是典型案例。仅需铁磁性、晶格手性和反对称交换这几项要素，在特定温度与磁场组合条件下 13 13 ^(13){ }^{13} ，便能形成分层的"斯格明子晶体"相。因此，这种表面复杂的磁结构实际上能用极少的微观相互作用简明描述——通过从原子位置转向原子相互作用的视角，系统复杂性便得到了根本性简化。由此引出一个明显问题：图 1a-d 所示 PMN 的分层结构是否也可能源于相对简单的相互作用？事实上，文献 14 14 ^(14){ }^{14} 已建立了基于相互作用的 PMN 模型，学界必然期待将该研究结果与近期 RMC 工作进行对比。尤其若能证明两者得出的实空间描述本质等价，那么图 1a-d 呈现的结构复杂性便完全源自
combination of simple cation-ordering rules and the interactions between neighbouring Pb − O , Mg − O , Nb − O Pb − O , Mg − O , Nb − O Pb-O,Mg-O,Nb-O\mathrm{Pb}-\mathrm{O}, \mathrm{Mg}-\mathrm{O}, \mathrm{Nb}-\mathrm{O} and O − O O − O O-O\mathrm{O}-\mathrm{O} atom pairs. Having reduced the system to these few parameters, one might more straightforwardly assess how to vary these parameters to control the relaxor state.
通过简单的阳离子有序规则与邻近 Pb − O , Mg − O , Nb − O Pb − O , Mg − O , Nb − O Pb-O,Mg-O,Nb-O\mathrm{Pb}-\mathrm{O}, \mathrm{Mg}-\mathrm{O}, \mathrm{Nb}-\mathrm{O} 和 O − O O − O O-O\mathrm{O}-\mathrm{O} 原子对相互作用的组合，将系统简化为这几个参数后，或许能更直接评估如何调整这些参数来控制弛豫态。
In this context, perhaps the bigger challenge in complex materials science is to develop general methodologies for finding the right interaction model and corresponding theory that allow complex structures and their underlying physics to be understood as simply as possible. Whereas historical approaches have relied heavily on the personal insight of key individuals in the field 12 12 ^(12){ }^{12}, machine-learning approaches might offer an opportunity to capture this insight and make it more widely available. One might also learn from the frustrated magnetism community, where mean-field theory is exploited to fit the data for complex magnetic states directly in terms of pairwise interactions, avoiding the generation of atomistic models altogether 15 15 ^(15){ }^{15}. There seems an obvious opportunity to extend such methods to non-magnetic systems.
在此背景下，复杂材料科学领域更大的挑战或许是开发通用方法论，以寻找合适的相互作用模型及相应理论，从而尽可能简单地理解复杂结构及其基础物理机制。传统方法高度依赖该领域关键人物的个人洞见 12 12 ^(12){ }^{12} ，而机器学习方法可能为捕捉这种洞见并使其更广泛可用提供契机。我们或可借鉴阻挫磁学研究领域的经验——该领域利用平均场理论直接通过成对相互作用拟合复杂磁态数据，完全避免了原子模型的构建 15 15 ^(15){ }^{15} 。将这些方法拓展至非磁性体系显然存在显著机遇。

Acknowledgements  致谢

The author gratefully acknowledges funding from the E.R.C. (Grant 788144).
作者衷心感谢欧洲研究委员会（ERC Grant 788144）提供的资助支持。
Received: 27 June 2019; Accepted: 2 September 2019; Published online: 01 October 2019
收稿日期：2019 年 6 月 27 日；录用日期：2019 年 9 月 2 日；网络首发：2019 年 10 月 1 日

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  1. 1 1 ^(1){ }^{1} Department of Chemistry, University of Oxford, Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QR, UK. *email: andrew.goodwin@chem. ox.ac.uk
    1 1 ^(1){ }^{1} 英国牛津大学化学系无机化学实验室，南园路，牛津 OX1 3QR。*电子邮箱：andrew.goodwin@chem. ox.ac.uk