ORIGINAL RESEARCH published: 13 November 2017 doi: 10.3389/fmats.2017.00034 Assessing Local Structure Motifs Using Order Parameters for Motif Recognition, Interstitial Identification, and Diffusion Path Characterization Nils E. R. Zimmermann 1*, Matthew K. Horton 2,3, Anubhav Jain 3 and Maciej Haranczyk 1 1Lawrence Berkeley National Laboratory, Computational Research Division, Berkeley, CA, United States, 2Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA, United States, 3Lawrence Berkeley National Laboratory, Energy Technologies Area, Berkeley, CA, United States Structure–property relationships form the basis of many design rules in materials science, including synthesizability and long-term stability of catalysts, control of electrical and opto- electronic behavior in semiconductors, as well as the capacity of and transport properties in cathode materials for rechargeable batteries. The immediate atomic environments (i.e., the first coordination shells) of a few atomic sites are often a key factor in achieving a Edited by: desired property. Some of the most frequently encountered coordination patterns are Zhenyu Li, University of Science and Technology tetrahedra, octahedra, body and face-centered cubic as well as hexagonal close packed- of China, China like environments. Here, we showcase the usefulness of local order parameters to identify Reviewed by: these basic structural motifs in inorganic solid materials by developing classification Yi Liu, criteria. We introduce a systematic testing framework, the Einstein crystal test rig, that Shanghai University, China Zhen Zhou, probes the response of order parameters to distortions in perfect motifs to validate our Nankai University, China approach. Subsequently, we highlight three important application cases. First, we map Jun Jiang, University of Science and Technology basic crystal structure information of a large materials database in an intuitive manner of China, China by screening the Materials Project (MP) database (61,422 compounds) for element- *Correspondence: specific motif distributions. Second, we use the structure-motif recognition capabilities Nils E. R. Zimmermann to automatically find interstitials in metals, semiconductor, and insulator materials. Our [email protected] Interstitialcy Finding Tool (InFiT) facilitates high-throughput screenings of defect properties. Specialty section: Third, the order parameters are reliable and compact quantitative structure descriptors This article was submitted to for characterizing diffusion hops of intercalants as our example of magnesium in MnO2- Computational Materials Science, a section of the journal Frontiers in spinel indicates. Finally, the tools developed in our work are readily and freely available Materials as software implementations in the pymatgen library, and we expect them to be further Received: 13 July 2017 applied to machine-learning approaches for emerging applications in materials science. Accepted: 18 October 2017 Published: 13 November 2017 Keywords: materials science, crystal structure, descriptors, databases, interstitials, intercalation, diffusion Citation: Zimmermann NER, Horton MK, Jain A 1. INTRODUCTION and Haranczyk M (2017) Assessing Local Structure Motifs Using Order Crystals consist of atoms that are arranged in periodic patterns in three dimensions (Sands, 1993). Parameters for Motif Recognition, This regular arrangement is called the crystal structure which, together with the chemical composi- Interstitial Identification, and Diffusion Path Characterization. tion, dictates the properties of a material (Morris, 2007). Typically, the crystal structure is described Front. Mater. 4:34. with approximations and abstractions (Morris, 2007). One approach is to focus on the immediate doi: 10.3389/fmats.2017.00034 surrounding of each atom (first coordination shell) and to use the number of surrounding atoms Frontiers in Materials | www.frontiersin.org 1 November 2017 | Volume 4 | Article 34 Zimmermann et al. Assessing Motifs Using Order Parameters (coordination number) and the pattern (structure motif) for of motif resemblance, thus, being a deterministic method. Note structure description, the discipline of which was coined by that the MC-based approach is expected to be much more time- Werner and which is today known as coordination chemistry consuming than the order parameter route. (Werner, 1912). Among frequently occurring structure motifs are We here develop an effective and computationally efficient tetrahedra, octahedra, body-center and face-centered cubic as well approach for finding atomic neighbors and identifying motif types as hexagonal close-packed motifs (Figure 1). in inorganic materials using order parameters (Steinhardt et al., The occurrence of basic structural motifs in crystalline com- 1983; Peters, 2009; Zimmermann et al., 2015) for pattern match- pounds has been shown to be important indictors for predict- ing. Furthermore, we introduce a testing framework (Einstein ing materials properties in several scientific and technological crystal test rig) for validation of any such motif-finding effort. We contexts. Finding and quantitatively assessing primary building then apply our approach to the database provided by the Materials blocks of zeolite materials (SiO4 tetrahedra) can be used to predict Project (Jain et al., 2013), where we use well-defined materials the feasibility of synthesizing a (hypothetical) material (Li et al., subsets for testing. Finally, the method is used to generate crystal 2013; Mazur et al., 2015) and to rate their likelihood for indus- structure representations of the Materials Project database, to trial deployment—for example, as a catalyst—(Zimmermann and determine potential interstitial sites in several materials, and to Haranczyk, 2016). Design rules for novel battery materials are quantitatively characterize the coordination environment change frequently developed employing information about the coordi- along the jump-diffusion path of an intercalating ion. nation pattern of the migrating ion (Rong et al., 2015) and the host structure (Li et al., 2009; Wang et al., 2015). Models based 2. METHODS on structural fragments can be used to assess influencing fac- tors to the superconductivity critical temperature (Isayev et al., We focus on local structural motifs that are based on a central 2015). Interstitials in dense inorganic materials are frequently atom and its first coordination shell. The two basic steps in found in positions where the interstitials assume tetrahedrally or identifying structural motifs are therefore: octahedrally coordinated positions (Decoster et al., 2008, 2009a,b, 1. finding bonded neighbors and 2010a,b, 2012; Pereira et al., 2011, 2012; Amorim et al., 2013; Silva 2. motif recognition. et al., 2014). Screening large databases for structure motif occurrence has More complex patterns such as those involving second-shell hence the potential to find new candidate materials for various neighbors and cyclic motifs (rings) would require a more extensive emerging applications. The inherent difficulty is to develop recog- analysis of the connectivity between atoms. nition tools that allow for reliable and rapid motif identification. There are two basic steps involved in the (automatic) identifica- 2.1. Bonding Identification tion of a coordination motif around a given atom: (i) neighbor Bonds are determined on the basis of the distance, di,j, between finding and (ii) pattern matching. Neighbors can be found on two atoms i and j: k − k the basis of interatomic distances—possibly in combination with di;j = pi pj ; (1) typical bond lengths (Brunner, 1977; Hoppe, 1979; O’Keeffe and where pi is the position of atom i. We systematically investigate Brese, 1991)—or by a topology-based approach (Dirichlet, 1850; three different neighbor-finding methods, all of which work with a Voronoi, 1908; Mickel et al., 2013). For pattern matching, there site-specific cutoff distance, rcut,i. In the first method (“min_dist”), exist two popular conceptual approaches: (i) using Monte Carlo we determine the (absolute) distance to the nearest neighbor, (MC) moves (Shetty et al., 2002) and (ii) using order parameters dmin,i, of a given site i and, subsequently, we consider all additional (Steinhardt et al., 1983; Peters, 2009; Zimmermann et al., 2015). sites that are at maximum rcut,i = (1 + δ)dmin,i apart from site i In the MC approach, an ideal structure motif is placed onto a (Figure 2), where δ denotes a (relative) neighbor-finding tolerance central atom and its neighbors, and the ideal motif’s position (distance). The other two approaches work similarly, except for and size are varied to yield a small root mean square deviation ~ the fact that we use dimensionless distances, di;j = di;j=li;j, between the positions of the ideal motif and the neighbors of the where l is a length being characteristic for the considered pair of central atom. In the systematically expandable (Santiso and Trout, atoms i and j. The following two approaches for the characteristic 2011) order parameter approach, the bond angles of a given motif length are tested: the sum of atom (or, ion) radii (Shannon (1976); are used in mathematical functions to directly yield a measure atom atom “min_VIRE”: li;j = ri + rj ) and the typical bond length bond (O’Keeffe and Brese (1991); “min_OKeeffe”: li;j = li;j ). The radii are calculated with a valence-ionic radius estimator (VIRE) implemented in pymatgen (Ong et al., 2013). The estimator uses