doi.org/10.26434/chemrxiv.7580021.v1
Single Crystal Automated Refinement (SCAR): A Data-Driven Method for
Solving Inorganic Structures
Gayatri Viswanathan, Anton Oliynyk, Erin Antono, Julia Ling, Bryce Meredig, Jakoah Brgoch
Submitted date: 11/01/2019 • Posted date: 14/01/2019 Licence: CC BY-NC-ND 4.0
Citation information: Viswanathan, Gayatri; Oliynyk, Anton; Antono, Erin; Ling, Julia; Meredig, Bryce; Brgoch, Jakoah (2019): Single Crystal Automated Refinement (SCAR): A Data-Driven Method for Solving Inorganic Structures. ChemRxiv. Preprint.
Single crystal diffraction is one of the most common experimental techniques in chemistry for determining a crystal structure. However, the process of crystal structure solution and refinement is not always
straightforward. Methods to simplify and rationalize the path to the most optimal crystal structure model have been incorporated into various data processing and crystal structure solution software, with the focus
generally on aiding macromolecular or protein structure solution. In this work, we propose a new method that uses single crystal data to solve the crystal structures of inorganic, extended solids called “Single Crystal Automated Refinement (SCAR).” The approach was developed using data mining and machine-learning methods and considers several structural features common in inorganic solids, like atom assignment based on physically reasonable distances, atomic statistical mixing, and crystallographic site deficiency. The output is a tree of possible solutions for the data set with a corresponding fit score indicating the most reasonable crystal structure. Here, the foundation for SCAR is presented followed by the implementation of SCAR to solve two newly synthesized and previously unreported phases, ZrAu0.5Os0.5 and Nd4Mn2AuGe4. The structure solutions are found to be comparable with manually solving the data set, including the same refined mixed occupancies and atomic deficiency, supporting the validity of this automatic structure solution method. The proposed SCAR program is thusly verified to be a fast and reliable assistant in solving even complex single crystal diffraction data for extended inorganic solids.
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Single Crystal Automated Refinement (SCAR): A Data-Driven Method for Solving Inorganic Structures
Gayatri Viswanathan,† Anton O. Oliynyk,*,† Erin Antono,‡ Julia Ling,‡ Bryce Meredig,‡
Jakoah Brgoch*,†
† Department of Chemistry, University of Houston, Houston, TX 77204 USA ‡ Citrine Informatics, Redwood City, CA 94063 USA
Abstract
Single crystal diffraction is one of the most common experimental techniques in chemistry for determining a crystal structure. However, the process of crystal structure solution and refinement is not always straightforward. Methods to simplify and rationalize the path to the most optimal crystal structure model have been incorporated into various data processing and crystal structure solution software, with the focus generally on aiding macromolecular or protein structure solution. In this work, we propose a new method that uses single crystal data to solve the crystal structures of inorganic, extended solids called “Single Crystal Automated Refinement (SCAR).” The approach was developed using data mining and machine-learning methods and considers several structural features common in inorganic solids, like atom assignment based on physically reasonable distances, atomic statistical mixing, and crystallographic site deficiency. The output is a tree of possible solutions for the data set with a corresponding fit score indicating the most reasonable crystal structure. Here, the foundation for SCAR is presented followed by the implementation of SCAR to solve two newly synthesized and previously unreported phases, ZrAu0.5Os0.5 and Nd4Mn2AuGe4. The structure solutions are found to be comparable with manually
1. Introduction
X-ray diffraction1 has become an essential characterization method to determine the crystal structures of compounds ranging from organic molecules to inorganic solids.2 X-ray crystallography has helped researchers determine typical radii of atoms, understand chemical bonds, and confirm existing theories about solid-state structures.3 Indeed, single crystal diffraction
has become one of the most used experimental techniques in most sub-disciplines of chemistry from early materials characterization to modern drug design.4–6
In the current study, we present a new approach for automatically solving the single crystal structures of extended inorganic solid through a program called, Single Crystal Automated
Refinement (SCAR). This method solves crystal structures using a unique approach that includes
atom assignment based on physically reasonable distances, rather than solely based on electron density. SCAR also considers atomic statistical mixing and the possibility of crystallographic site deficiency, i.e., vacancies, to arrive at the final crystal structure. This solution process specifically makes use of data mining and machine learning models that have been trained on the data of known crystal structures to predict the bond lengths, and data mining models for probability of site mixing and partial occupancy. The program creates a tree of different crystal structure options (graphically visualized); each with an associated fit score so that the relative fits of different possible structures can also be systematically compared. In this paper, we first introduce the methodology behind
SCAR. We then showcase the capabilities of this new method by synthesizing two inorganic crystal
structures, Nd4Mn2AuGe4 and ZrAu0.5Os0.5, and solving their crystal structure manually (the
traditional approach) and automatically (with SCAR). The resulting crystal structure solutions are indistinguishable, which supports the effectiveness of using SCAR as an aid for solving crystal structures ranging from relatively simple cubic phases to complex inorganic solids.
2. Methodology
2.1 SCAR Method Development
The optimization model is built in python; it uses the SHELXTL software package15 to perform single crystal diffraction data refinement and uses graphviz16 to visualize the optimization process. The automated refinement process requires only two input files, the *.ins (instruction file) and *.hkl (observed data) files, which are generated by SHELXTL once data correction, preprocessing and merging are completed. Similar to previously developed automated refinement methods, this algorithm also requires the approximate elemental composition of the structure. In most cases, simply listing the elements and the nominal stoichiometry expected in the structure is sufficient. The actual stoichiometry is not required; however, the option to have rigid boundaries could be incorporated to penalize large deviations from the nominal composition. The algorithm then uses direct methods (TREF command in the *.ins file) to propose an initial structure model with the ensuing step-by-step refinement occurring based on the expected interatomic distances as well as the conventional R-factor (R1 score), which quantifies the agreement between experimental diffraction data and the values calculated from the crystallographic model. The typical refinement steps of SCAR are shown in Figure 1. The behavior of the optimization algorithm can be controlled through a number of parameters. For example, one such parameter, score_weighting, adjusts the tradeoff between R1 score and bond length score when evaluating the quality of a given structure. The parameters can all be modified from their default values based on an expert user’s evaluation of the SCAR results. The source code for the program, along with installation and usage instructions can be found on Github (https://github.com/CitrineInformatics/crystal-refinement).
structure solutions. Therefore, SCAR augments the structure solution process by enumerating multiple solution paths in a tree structure to reduce the probability of erroneous crystal structure solutions. For example, in a complex, polyatomic crystal structure there are many possible permutations of assigning the atoms to each crystallographic site. While some assignments can be immediately ruled out due to unrealistic interatomic distances, poor refinement statistics, or just based on chemical intuition, there are often multiple feasible options. In this case, SCAR will simultaneously explore multiple branching paths. As the optimization continues and more paths are generated, the paths are pruned based on bond length agreement and the R1 value. Using a similar process, the optimizer also explores site mixing and partial occupancy at each crystallographic site. These parameters are usually challenging for scientists to explore during manual refinements because of the sheer number of possible options; however, the automated process can quickly examine all possibilities with little additional effort. At the end of the optimization, the program presents the user with a set of most likely solutions, along with the best path.
Figure 1. Single crystal refinement process fused
for structure solution by the Single Crystal
Automated Refinement (SCAR) method. 2.2 Synthesis
To experimentally validate SCAR, including testing the mixing/deficiency refinement capabilities, two compounds were synthesized. ZrAu0.5Os0.5 was selected because it should form
a simple crystal structure and contain Au/Os atomic mixing, whereas Nd4Mn2AuGe4 was selected
“ZrAu0.5Os0.5” were prepared from the elements (0.2 g total mass) by first cold-pressing into pellets
(6 mm diameter) and then melting two times in a Centorr arc furnace on a water-cooled copper hearth under an argon atmosphere. The weight loss after arc melting was less than 1%. The arc melted ZrAu0.5Os0.5 and Nd4Mn2AuGe4 ingots were each sealed in evacuated fused-silica tubes
and annealed at 800˚C for one week, followed by quenching in cold water; this route led to the best sample crystallinity. Varying the annealing time and temperature did not produce to any discernable changes in the product’s crystal quality. The annealed samples were crushed and ground into a fine powder for analysis by powder X-ray diffraction, which was collected on a PanAnalytical X’Pert powder diffractometer (Cu Kα radiation, 1.54183 Å). A qualitative analysis of these data was accomplished by comparing the experimental diffractograms to the calculated powder patterns generated based on the crystal structure manually refined from single crystal diffraction experiment.
2.4 Crystal Structure Determination
Sufficiently large single crystals of Nd4Mn2AuGe4 and ZrAu0.5Os0.5, which were both gray
and irregularly shaped, were manually picked from the crushed ingot using an optical microscope for analysis by single crystal diffraction. Intensity data were collected on a Bruker D8 X-ray diffractometer equipped with SMART APEX II CCD area detector and a Mo Kα radiation source. Face-indexed numerical absorption corrections were applied. Structure solution and refinement were carried out using the SHELXTL program package (version 6.12).15The crystal structures of both compounds were manually-refined, i.e., following conventional refinement approaches, as well as refined using SCAR.
ZrAu0.5Os0.5 single crystal data was analyzed and the centrosymmetric cubic space group
𝑃𝑚3̅𝑚 was chosen based on Laue symmetry, systematic absences, and intensity statistics. Direct methods revealed the initial atomic positions corresponding to the CsCl-type structure (Figure 2). Crystal data and further details are included in Table 1. The final positional and displacement parameters are found in Table 2, and selected interatomic distances are given in Table 3. The centrosymmetric monoclinic space group C2/m was chosen for Nd4Mn2AuGe4 based on Laue
symmetry, systematic absences, and intensity statistics. Direct methods revealed the initial atomic positions corresponding to the Ho4Ni2InGe4-type structure (Figure 3).17 Atomic coordinates were
standardized with use the of the program STRUCTURE TIDY.18 The manual structure refinements
of Nd4Mn2AuGe4 were not straightforward, because the displacement parameters for the Au site
were consistently larger compared to other sites. Successive manual refinements indicated partial occupancy or 0.627(7) for the Au site, in contrast to full occupancies for the remaining sites. This partial occupancy was also identified using SCAR. The idealized formula Nd4Mn2AuGe4 will be
used in the subsequent discussion, but the nonstoichiometric formula Nd4Mn2Au1-xGe4 is
Figure 2. Structure of ZrAu0.5Os0.5 viewed along the c direction.
Figure 3. (a) Structure of Nd4Mn2AuGe4 highlighting the [Mn2AuGe4] bonding network, viewed
along the b direction.
Table 1. Crystallographic data for ZrAu0.5Os0.5.
Manually-Refined SCAR-Refined Formula ZrAu0.5(1)Os0.5(1) ZrAu0.5(1)Os0.5(1)
Formula mass (g mol-1) 284.80 Space group Pm3̅m (No. 221)
a (Å) 3.318(9) V (Å3) 36.5(2) Z 1 calc (g cm–3) 12.952 T (K) 273 Crystal dimensions (mm) 0.08 0.05 0.03
Radiation Graphite monochromated Mo K, = 0.71073 Å
(Mo K) (mm–1) 100.014
Transmission factors 0.0435 – 0.1421
2 limits 12.30 – 66.22
Data collected –5 h 5, –5 k 3, –4 l 4
No. of unique data, including Fo2 < 0 28 (Rint = 0.0402)
No. of unique data, with Fo2 > 2(Fo2) 28
No. of variables 5 (6) 6 R(F) for Fo2 > 2(Fo2) a 0.0258 (0.0254) 0.0253 Rw(Fo2) b 0.0258 (0.0254) 0.0253 Goodness of fit 1.359 (1.357) 1.793 ()max, ()min (e Å–3) 1.369, −1.273 (1.379, −1.277) 1.364, −1.028 a . b ; where .
Table 2. Atomic coordinates for ZrAu0.5Os0.5.
Atom Wyck. occ. x y z Ueq (Å2)a
(a) Manually-Refined Zr 1b 1.01(3)b 1/2 1/2 1/2 0.025(1) Au 1a 0.5(1) 0 0 0 0.0293(8) Os 1a 0.5(1) 0 0 0 0.0293(8) (b) SCAR-Refined Zr 1a 1.02(2) 0 0 0 0.025(2) Au 1b 0.5(1) 1/2 1/2 1/2 0.0294(9) Os 1b 0.5(1) 1/2 1/2 1/2 0.0294(9) a U
eq is defined as one-third of the trace of the orthogonalized Uij tensor.
b Originally, occupancy was not refined but is also included to compare with the SCAR results
Table 3. Selected interatomic distances (Å) for ZrAu0.5Os0.5.
Manually-Refined SCAR-Refined Zr—Au/Os (8) 2.873(8) 2.873(8) Zr—Zr (6) 3.318(9) 3.318(9) Au/Os—Au/Os (6) 3.318(9) 3.318(9)
Table 4. Crystallographic data for Nd4Mn2AuGe4.
Manually-Refined SCAR-Refined Formula Nd4Mn2Au0.627(7)Ge4 Nd4Mn2Au0.622(7)Ge4
Formula mass (g mol-1) 1100.902 1099.917
Space group C2/m (No. 12)
β (˚) 106.63(1) V (Å3) 496(1) Z 2 calc (g cm–3) 7.377 T (K) 296 Crystal dimensions (mm) 0.01 0.01 0.01
Radiation Graphite monochromated Mo K, = 0.71073 Å
(Mo K) (mm–1) 43.688
Transmission factors 0.609-0.615
2 limits 8.86 – 63.18
Data collected –22 h 23, –6 k 6, –10 l 10 No. of data collected 2967
No. of unique data, including Fo2 < 0 899 (Rint = 0.0883)
No. of unique data, with Fo2 > 2(Fo2) 589
No. of variables 37 R(F) for Fo2 > 2(Fo2) a 0.0539 0.0472 Rw(Fo2) b 0.0932 0.0939 Goodness of fit 1.032 0.684 ()max, ()min (e Å–3) 4.101, −3.605 3.837, −2.871 a . b ; where . a U
eq is defined as one-third of the trace of the orthogonalized Uij tensor.
F Fo Fc Fo R
1/2 4 o 2 2 c 2 o 2 o w F wF F wF R w
Fo2 Ap2Bp
2 1
3 2 0 , max c2 2 o F F p Table 5. Atomic coordinates for Nd4Mn2AuGe4.
Table 6. Selected interatomic distances (Å) for Nd4Mn2AuGe4. Manually-Refined SCAR-Refined Manually-Refined SCAR-Refined Nd1−Ge1 (3) 3.025(3) 3.024(3) Nd2−Ge2 (4) 3.154(3) 3.154(3) Nd1−Ge2 3.107(4) 3.107(4) Nd2−Mn (2) 3.268(5) 3.267(5) Nd1−Ge2 (4) 3.119(3) 3.119(3) Nd2−Mn (3) 3.279(3) 3.279(3) Nd1−Mn (2) 3.353(4) 3.353(4) Nd2−Au (6) 3.414(3) 3.414(3) Nd1−Mn (3) 3.485(3) 3.486(3) Ge1−Ge1 2.566(5) 2.569(5) Nd1−Au (5) 3.429(3) 3.429(3) Ge1−Mn 2.613(5) 2.614(5) Nd1−Nd2 (2) 3.692(4) 3.692(4) Ge1−Au (2) 2.955(4) 2.954(4) Nd1−Nd1 3.785(4) 3.784(4) Mn−Ge2 (3) 2.605(3) 2.604(3) Nd2−Ge1 (3) 3.113(3) 3.114(3) Mn−Ge2 (2) 2.685(5) 2.685(5) Nd2−Ge1 (4) 3.150(3) 3.150(3) Mn−Mn (2) 3.222(5) 3.221(5)
3. Results and Discussion
3.1 Foundation of the SCAR Method and Creation of Data Driven Models for Bond Length, Site Mixing, and Partial Occupancy
Refining organic crystal structures can be a tedious process, but there are many opportunities to simplify the process using constraints based on structural similarities of other organic molecules. For example, an aromatic ring can be easily reconstructed once the position of one atom is known, because of the known angles and distances between hydrogen and carbon atoms. These same assumptions allow computer programs to (at least partially) solve crystal structures with relative ease. On the other hand, solving and refining structures of extended inorganic solids from single crystal diffraction data, taking into account atomic mixing and deficiency, has never been automated. In part, the lack of automation is due to the comparatively small field of solid-state materials research. Furthermore, the difference between extended inorganic solids and small molecule crystal structures is significant. The large number of electrons (from heavy elements) in extended solid-state structures results in high scatter, which produces a noisier background making it difficult to assign atom positions correctly. Low-intensity background peaks could be mistakenly assigned as atoms even though the peaks could be noise from an inadequate absorption correction. To account for this issue, researchers solving inorganic structures often focus on the residual peak/holes using a differential Fourier map (a method to convert reciprocal diffraction data into a real space crystal structure). The solution is considered acceptable if the values of residual peak/holes stay within of 10% of electron density of the most electron-rich atom, which can reach the values up to 5-8 electrons per cubic Ångstrom.19–21For
The R1 agreement factor provides significant information when determining the correctness of initial models towards the final structure solution. However, R1 values can be misleading near the final steps of the structural refinement. Indeed, proposed structure models could have a high mathematical agreement (low R1 value), but do not make chemical sense, e.g., containing unreasonable bond lengths. Therefore, balancing between chemical intuition and statistical agreement is an essential step in automated refinement. The SCAR procedure was designed to address the fact that the lowest R1 value does not always represent a structure that makes sense from a chemical perspective by also examining interatomic distances in the structure solution. This will prevent the automatic solution from incorrectly assigning atoms to peaks that could mimic the presence of light elements but with bond lengths that are too short for any physical interpretation.
To aid the creation of a scheme capable of predicting interatomic distances in an unknown compound, SCAR employs data mining and machine learning. Machine learning and data mining have been successfully applied to materials problems across various domains. For example, they have been used to successfully identify new shape memory alloys,22 ferroelectric materials,23 and
novel thermoelectrics,24–26 to make property predictions for heat capacity,27–28 band gap of crystalline solids,29 and elastic moduli,30 to optimize solar cells,31 predict new phosphor materials,32 and to classify crystal structures of inorganic compounds.33–38 These methods generate predictions for unknown examples based on statistical relationships and patterns discovered using reliable data, informative descriptions of that data, and machine-learning algorithms. In this work, we use a machine learning approach to build predictive models for interatomic distances. The bond length model uses the formula of the compound (encapsulating information on the type of compound, e.g., ionic, Zintl phases, or intermetallic) as well as the composition of the two atomic sites (encapsulating information on chemistry, deficiency, and mixing) as inputs, and predicts the most likely nearest neighbor distance. The site compositions and formula are represented using chemical descriptors (e.g., electronegativity, number of valence electrons, or position on the periodic table) available on the Citrination platform.39–43 A heuristic bond length estimate generated by summing the average atomic radii for the sites was also calculated as an additional descriptor. Machine-learning and data mining algorithms is a significant step forward for the current single crystal-based approach, compared to previous automated crystal structure solutions; for example, solving structures from powder diffraction data in a hybrid DFT-experimental way.44
Another difficulty that arises in the crystal structure solution of extended inorganic solids, which is different from organic molecules, is that the former often contains defects like site deficiency and statistical atomic mixing. These structural features in a solid can be crucial for the physical properties; for example, atomic mixing is one of the most fundamental ways to control transport properties (electrical conductivity and thermal conductivity),48 atomic mixing via doping
is an important way to tune the band gap in semiconductors,49 and crystallographic site deficiency is central for ion mobility in batteries.50 These essential atomic mixing and deficiency features make the previously proposed organic-focused automated crystal structure solution methods impractical to use for solving solid-state inorganic structures. Thus, the creation of an automated refinement for extended inorganic crystal structures must also pay specific attention to accounting for crystal structure defects.
Two additional models were therefore created using the assistance of data mining and machine learning to determine this probability for atomic mixing and site deficiency in a crystal structure. These models were built by analyzing crystal structure data contained in Pearson’s Crystal Database (PCD).51 A total of 92,938 compounds (9.5% binary, 35.1% ternary, 34.9%
quaternary, 20.5% higher element-count compounds) with the corresponding number of elements in the formula were first extracted from PCD. The data were initially sanitized through a multistep process. The first step was to remove all duplicate formulae entries and formulae containing square brackets. Compounds with exotic elements, e.g., deuterium, argon, and plutonium, as well as all entries with nonspecific stoichiometries, e.g., index x, were also removed, leaving 61,289 remaining compounds. The composition information was subsequently split into the component elements and indices.
These data were then analyzed for atomic mixing as well as the presence of atomic deficiency. Overall, 43,170 compounds (70%) were found to contain atomic mixing on at least one crystallographic position whereas 11,296 compounds (18%) were found to be deficient, i.e., contain vacancies. From the latter set of crystal structures, the maximum observed deficiencies for each element were determined; this step was limited to compositions with up to four elements to reduce the complexity of the calculations. A flowchart representing the sanitizing process is shown in Figure S1. Finally, the probability for atomic mixing was determined for each element pair by comparing the number of mixing occurrences to the total number of occurrences of the elements of this pair in known compounds in Pearson’s Crystal Database. Similarly, the probability for atomic deficiency was determined for each element by comparing the number of deficient occurrences to the total number of occurrences of the element. The site deficiency and atomic mixing models can also be used independently on Citrine Informatics website.39
statistics), but also implementing physically reasonable interatomic distances and taking into consideration structural defects common for intermetallic compounds.
3.2 Implementation of the SCAR Method to Analyze and Solve Two Crystal Structures
The SCAR program was validated by subsequently synthesizing two inorganic solids, ZrAu0.5Os0.5, which is predicted to have a relatively simple crystal structure with Au and Os atomic
mixing, and Nd4Mn2AuGe4, that is predicted to adopt a complex inorganic crystal structure that
contains gold vacancies.
The case of ZrAu0.5Os0.5
To examine the validity of identifying atomic mixing with SCAR, elements that statistically mix with Au were identified. The probability of Au atoms to mix with other elements is represented on the periodic table visualized in Figure 4, based on the data mining approach described above. The percentage in each square indicates the ratio of mixing occurrences to the total number of compounds. It is evident from the data that Au tends to mix with p-block metalloid elements and most of transition metal series, with the exception of early transition metals. There is a minimal probability of Au mixing with s-block elements or the rare-earth elements. It is also interesting to recognize that gold has a high probability (50.0%) to mix with Os but that there is no precedent for Au to mix with Re. This surprising anomaly of Au/Os but not Au/Re mixing was, therefore, investigated to ensure the prediction of statistical mixing is robust.
Figure 4. Mixing probabilities for Au-containing pair in inorganic extended structures. The
Two samples that contain these pairs of elements, Au-Os and Au-Re, were reacted in combination with zirconium, which is known to form phases with all three heavy transition metals. The prediction is that the former combination of elements should contain mixing whereas the latter group of elements will not contain mixing. Analyzing the samples using powder X-ray diffraction shows that ZrAu0.5Os0.5 phase was formed as a pure phase product and that the structure is a
CsCl-type structure with one atomic site shared by Au and Os as predicted, as shown in Figure 5. ZrAu0.5Os0.5 was then analyzed using semi-quantitative EDX, which indicates the composition is
52.7 mol% Zr, 21.6 mol% Os, 25.7 mol% Au, in agreement with the nominal composition. Moreover, the elements are uniformly distributed in the sample indicating atomic mixing, as shown in Figure S2. The attempt to synthesize a similar phase with a composition ZrAu0.5Re0.5 did not
result in a single phase product (Figure S3). Instead, a non-equilibrium mixture of binary phases was present in the sample, which confirms that statistical mixing between Re and Au does not occur under these synthesis conditions, and supports the predicted absence of atomic statistical mixing.
Figure 5. The powder X-ray diffractogram shows ZrAu0.5Os0.5 is obtained as a pure phase product.
Given that the algorithm developed to identify the potential for atomic mixing was independently successful, the full SCAR program was used to solve the single crystal structure of ZrAu0.5Os0.5, and the solution was compared to a manual (classical) crystal structure refinement.
The structure refinement for ZrAu0.5Os0.5 single crystal diffraction data, performed by the SCAR
and Zr in the same, originally assigned position, instead of switching Au with Os (R1 0.0306 vs.
R1 0.0315). Proceeding with the refinement, typically the extinction coefficient (highly important
for intermetallics) and anisotropic displacement parameters (unnecessary for cubic structures but fixed in the structure solution routine of the SCAR algorithm) are added. During this step of the refinement, a relatively high displacement parameter on the Au site indicates possible statistical mixture. Chemical intuition, used for manual structure solution, suggests that Au/Os mixture is more probable than Au/Zr, based on size and position in the periodic table. The SCAR algorithm also suggests the next step, Au/Os mixture, since data mining has revealed the probability of this is 50.0%, which is much higher than the probability of Au/Zr (2.4%) mixing (Figure 4). The refinement then proceeds further with statistical mixing applied and suggested weight added (Figure 6). The shown refinement tree represents a simplified version of possible refinement options available through the SCAR. A full version of the refinement tree with composition and stoichiometry taken into account is available in Figure S4, where the correct answer was reached in ten steps, identical to the steps shown in Figure 6, with only one additional step employed, refinement of occupancy on Zr site, in order to check if the starting stoichiometry (ZrAu0.5Os0.5)
Figure 6. SCAR-generated refinement tree for a simple ZrOs0.5Au0.5 structure generated by SCAR.
The R1 value indicates model fit (the difference between observed and calculated), the bond value indicates the placement of atoms at crystallographic sites based on relative interatomic distances, and overall is a combined score for taking into account all these parameters. The path to the best solution is highlighted in orange. The black paths are intermediate steps in the refinement. The models in blue are the terminate branches and highlight other possible solutions.
Comparing the SCAR refinement to the manual refinement shows the automated refinement has improved the accuracy of the refinement due to the inclusion of a sixth refinement parameter - occupancy of the Zr atom. While a similar accuracy could be achieved in the manual refinement by including this additional parameter (Table 1), most inorganic chemists would not be inclined to refine the Zr occupancy. R-value of 0.0253 in the SCAR output does not differ significantly from
R-value of 0.0258 in the manual refinement results. While both refinement methods result in the
CsCl-type structure for ZrAu0.5Os0.5, the Wyckoff positions and atomic positions of the Zr and
are interchangeable in the CsCl-type structure. Additionally, the SCAR-predicted equivalent isotropic displacement parameter Ueq of the atoms determined manually is within the acceptable
range of uncertainty or standard deviation. Therefore, SCAR provides the correct crystal structure solution compared to the manually solved structure. The SCAR gives a fast result (just minutes for a complete refinement tree) that can augment chemical intuition by providing a complete roadmap with all possible refinement pathways. This level of transparency makes SCAR not only a viable research program, but it is also a valuable teaching tool rather than a black box. With this example, we have tested SCAR with a simple crystal structure that contains only two crystallographic sites, three atoms, and six refined parameters.
The case of Nd4Mn2AuGe4
To test the ability of SCAR to solve more complex crystal structures, a quaternary Nd4Mn2AuGe4 compound was also synthesized. The compound is a new member of the quaternary
compounds adopting the Ho4Ni2InGe4-type structure. This crystal structure is of particular interest
here because it is not only a complex, polyatomic inorganic solid but the parent RE4Mn2InGe4
structure type is also known to contain vacancies; for example, the In site is only ≈87% occupied when RE = Gd.28,52,53
Nd4Mn2AuGe4 was synthesized as described with the powder X-ray diffraction pattern
revealing the desired phase is present in thermodynamic equilibria at 800 °C with NdAuGe and NdGe phases (Figure 7). Energy-dispersive X-ray (EDX) analysis was performed on a selected crystal on a JOEL JSM-6330F scanning electron microscope (Figure S5). This analysis yielded experimental compositions (25.63% Nd, 16.47% Mn, 8.75% Au, 49.15% Ge), which somewhat agree with the fully stoichiometric formula (36.4% Nd, 18.2% Mn, 9.1% Au, 36.4% Ge) and phase impurities.
Figure 7. The powder X-ray diffractogram shows the desired Nd4Mn2AuGe4 is produced as a
multiphase product with NdAuGe and NdGe.
full version of the tree diagram is shown in Figure S6, and a simplified version of this diagram is shown in Figure 8. The refinement started at a relatively low R1 value (0.1097), which indicated that most of the atomic positions were likely assigned correctly by SHELXTL program. The initial step in the refinement included deleting three atomic sites based on interatomic distances that were unreasonable. This did not result in significant improvement of R1 (0.1086); however, the new model was more chemically realistic, since the extremely short interatomic distances were eliminated. Indeed, the refinement of this complex crystal structure further highlights the importance of employing the bond distance model for structure solution, which is a contrast to more common brute-force R1 minimization techniques. Given that the information available for single crystal refinement is in a format of electron density, it easy to be misguided by electron density and assign atoms to crystallographic sites solely based on their Z number. The interatomic distance model gives an opportunity to justify atom assignment with a size factor. For example, the suggested distribution of atomic distances in the given class of compounds (intermetallic Nd– Mn–Au–Ge system) is visualized in Figure 9. The most crucial step in the correct site assignment is to put the correct atom into crystallographic position with the shortest distance to the neighbors. From the histograms, we can see that the shortest bond is expected to be between Ge–Ge atoms, with a median value of around 2.5–2.6 Å. With the second shortest distance in the structure Mn– Ge around 2.6 Å. The SCAR algorithm used this information to identify the correct atom locations. From the crystallographic table (Table 6), it is clear that the shortest interatomic distances are the Ge1–Ge1 contacts, which are separated by 2.566(5) Å as accurately predicted by the interatomic distance model. The second shortest distance in the structure is Mn–Ge2 at 2.605(3) Å, which again perfectly agrees with interatomic distance model prediction. If the interatomic distances for these contacts had fallen outside of this range, there is a high probability that the crystal structure solution needs to be revisited. The success of employing this bond distance model is also quantified by bond score (Figure 8 and Figure 10).
The next six steps performed by the SCAR algorithm were adjusting the atomic site assignment with reasonable atoms. More specifically, the Nd3 position was assigned to Ge3, Au2 was assigned to Nd2, the Au1 position was assigned as Nd1, Ge5 to Mn5, Ge6 to Ge6 (it remained the same), and Ge4 to Au4. Tweaking each crystallographic position resulted in a decrease in the overall score, which is a combination of R1 statistics, the bond distance score, and the element composition (Figure 10), as desired. Note that other automated refinement programs are typically dependent solely on the R1 value, and therefore would probably fall into a local minimum at step 3 (Figure 10). Overall, to solve this relatively complex structure, the SCAR algorithm has refined 489 models, which consist of 20 ranked probable solutions, with the correct solution (identical to manually solved answer) being ranked the first. The number of parameters refined for Nd4Mn2Au
1-xGe4 is 37; the SCAR-refined results are within the standard deviation of the manually-refined
Figure 8. Simplified SCAR-generated refinement tree for a more complex Nd4Mn2AuGe4 structure
Figure 9. Prediction of interatomic distances for
Nd4Mn2AuGe4 structure obtained from
citrination.com.
Figure 10. Visualization of atomic site assignment (first 7 steps of Figure 8) statistics, which rely
Figure 11. Deficiency probabilities for elements in inorganic extended structures determined from
the data mining model. The deficiency percentages are calculated from database statistics, where percent is the number of deficiency occurrences divided by the total number of compounds contained a given element.
Finally, analyzing the prevalence of site deficiency across the periodic table (Figure 11), it is evident that lithium, oxygen, and lighter main group elements are more likely to be deficient, which agrees with previous experimental reports. For example, structures with lithium vacancies are useful in preparing lithium ion batteries. Because the power of these batteries is dependent on deficient positions within the extended inorganic structure, porous membranes are incorporated in the batteries to allow for high mobility of lithium ions.54 Oxygen-deficiency in perovskites like
GdBaCo2O5.5 results in reduced symmetry within the inorganic structure; this distortion effects the
electromagnetic properties of the species and makes the compound useful for nanostructures or other industrial applications.55 The defective carbide structure in boron carbide is essential to its value as a material for engineering because the carbon deficiency yields unique mechanical properties, like hardness, that are independent of the structure’s atomic bonding and intrinsic properties.56 Other notable cases of deficient atoms include some of the metals like nickel, zinc, silver, and indium, known examples of solid-state ionic conductivity compounds. It is interesting to see that gold is one of the few 5d transition metals to also have a notable deficiency percentage (2.3%).
Comparing the manually refined structure and the SCAR refined results for Nd4Mn2AuGe4,
manual refinement; however, SCAR was able to easily attempt every refinement. The results showed that the manual structure refinement obtained a gold occupancy of 0.627(7) whereas the automated refinement suggested an occupancy of 0.622(7); these values are within the expected range of uncertainty and the slight difference in site occupancy results in a negligible variation in the formula mass between the two refinement results.
The resulting crystal structure solution is a relatively complex and large structure Nd4Mn2Au1-xGe4. Using the overall score statistics, which combines R1, expected composition
and reasonable interatomic distances, shows the final SCAR crystal structure solution is nearly identical to the manual crystal refinements. The atomic coordinates, equivalent isotropic displacement parameters, and selected interatomic distances in the Nd4Mn2AuGe4 structure from
both refinement methods are similar and generally vary by the expected standard deviation. To solve this relatively complex crystal structure, the SCAR algorithm refined 489 models, which consist of 20 ranked probable solutions, with the correct solution (identical to manually solved answer) ranked first. More importantly, the SCAR method was able to explore over 400 structural models sampling all variable in search of the correct crystal structure in only a couple of minutes. This provides significant justification for using this automated tool to solve complex crystal structures.
Conclusions
We created a new method for automated single crystal structure refinement with a specific focus on solving extended solid-state structures. This easy-to-use program, called Single Crystal
Automated Refinement (SCAR), is available as an open-source software at https://github.com/CitrineInformatics/crystal-refinement. The basis of SCAR consists of crystal structure solution features (supportive models for interatomic distances, deficiency, and site mixing) that have never been applied to automatically perform single crystal refinements. Employing data mining and predictive algorithms rooted in machine learning makes the program adaptive to specific classes of compounds, where structure defects or interatomic distances might deviate from average occurrence among all compounds. Experimental validation of the newly developed code was then carried out to show the versatility of SCAR. Indeed, two single crystal datasets were collected for two novel intermetallic compounds, ZrAu0.5Os0.5 and Nd4Mn2Au1-xGe4,
which were expected to feature atomic mixing and site deficiency, respectively. The SCAR algorithm shows a high accuracy and exceptional reproducibility of manual single-crystal refinement results, tested on previously unreported, novel intermetallic compounds with highly-symmetric small cell (ZrAu0.5Os0.5, cubic symmetry, 36.5 Å3 cell volume) and medium-size
low-symmetry cell (Nd4Mn2Au1-xGe4, monoclinic symmetry, 496 Å3 cell volume).
checking the correctness of the submitted structure for publications, similar to how CheckCIF warnings became a necessary piece of supporting information for single crystal data publishing. The proposed model has been validated with comparing manually solved and SCAR-solved structures, which feature site deficiency (Nd4Mn2AuGe4) and atomic mixing (ZrAu0.5Re0.5). These
results provide substantial evidence that SCAR is an ideal program to aid the crystal solution of inorganic solids, including accounting for common extended structure issues, such as site deficiency and atomic mixing.
Supporting Information
The supporting information contains X-ray crystallographic file in CIF format, data analysis scheme for creating a model for site deficiency/mixing, backscattered electron microscope image of ZrAu0.5Os0.5 at × 1000 magnification, experimental powder XRD pattern of ZrAu0.5Re0.5, a full
version of the refinement tree for ZrAu0.5Re0.5, backscattered electron microscope image of
Nd4Mn2AuGe4, a full version of the refinement tree for Nd4Mn2AuGe4. This material is available
free of charge via the Internet at http://pubs.acs.org.
Accession Codes
CCDC 1879788-1879791 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/ data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.
Author Information
Corresponding Author
*E-mail: [email protected], [email protected]
Notes
The authors declare no competing financial interest.
Acknowledgments
The authors thank National Science Foundation (CMMI 15-62142 and DMR 18-47701), the donors of the American Chemical Society Petroleum Research Fund (55625-DNI10), and Seed Funding for Advanced Computing (SeFAC) at the University of Houston for supporting this research. A.O.O. gratefully acknowledges the Eby Nell McElrath Postdoctoral Fellowship at the University of Houston for financial support. G.V. would like to thank the Summer Undergraduate Research Fellowship (SURF) at the University of Houston for funding that enabled this research experience.
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SUPPORTING INFORMATION
Single Crystal Automated Refinement (SCAR): A Data-Driven Method for Solving Inorganic Structures
Gayatri Viswanathan,† Anton O. Oliynyk,*,† Erin Antono,‡ Julia Ling,‡ Bryce Meredig,‡
Jakoah Brgoch*,†
Figure S1. Data analysis scheme for creating a model for site deficiency/mixing.
Figure S2. Backscattered electron microscope image of ZrAu0.5Os0.5 at × 1000 magnification.
Figure S3. Experimental powder XRD pattern of ZrAu0.5Re0.5.
(PDF of the figure is attached)
Figure S4. A full version of the refinement tree for ZrAu0.5Re0.5 with composition and
(a)
(b)
(c)
Figure S5. (a) Nd4Mn2AuGe4 Single Crystal at × 1000 magnification, (b) Electron
microscope image of Nd4Mn2AuGe4 at × 100 magnification, (c) Backscattered electron
microscope image of Nd4Mn2AuGe4 at × 1000 magnification. 20 μm
200 μm
Nd Mn AuGe (grey)4 2 4
20 μm
(PDF of the figure is attached)
Figure S6. A full version of the refinement tree for Nd4Mn2AuGe4 with composition and
download file view on ChemRxiv
