The AFLOW Library of Crystallographic Prototypes: Part 3

Abstract

The AFLOW Library of Crystallographic Prototypes has been extended to include a total of 1,100 common crystal structural prototypes (510 new ones with Part 3), comprising all of the inorganic crystal structures defined in the seven-volume Strukturbericht series published in Germany from 1937 through 1943. We cover a history of the Strukturbericht designation system, the evolution of the system over time, and the first comprehensive index of inorganic Strukturbericht designations ever published.

Introduction

Crystal structure classification began near the dawn of X-ray Crystallography with early works by Wyckoff [1], Ewald's 1927 Handbuch der Physik article [2], and the Landolt-Börnstein 1927 supplement [3]. In the next few decades, these catalogs proliferated, including the Strukturbericht (Structure Reports) series [4], Pearson's Handbook of Lattice Spacings and Structures of Metals and Alloys[5], [6], Smithells's Metals Reference Book[7], [8], and Wyckoff's updated Structure of Crystals[9]. In later years, Pearson's Handbook[10] and Smithells Metals Reference Book[11] acquired new editors and even today produce periodic editions. Subsequent works, such as the Gmelin Handbook[12], also appear regularly. As online access became the norm at the beginning of this century, electronic resources appeared, including the American Mineralogist Crystal Structure Database[13], which compiles the structures of minerals from a variety of sources, and the SpringerMaterials website [14], an extension of Pearson's Handbook that also incorporates the Landolt-Börnstein series.

Computational material-property databases have also become available: for example AFLOW (Automatic FLOW for Materials Discovery) [15], [16], [17], Novel Materials Discovery (NoMaD) [18], the Materials Project [19], and the Open Quantum Materials Database (OQMD) [20].

While these print and electronic databases contain a vast number of crystal structures, many are not optimized for use in materials computations, e.g., by providing structural information in a format which can be read by one of the common density functional computer codes. In addition, while most of these resources make their data available in standard formats, such as space group/Wyckoff positions or a Crystallographic Information File (CIF) [21], these forms still pose a challenge for novice researchers. Therefore, it is desirable to have a database that addresses both of these concerns.

The AFLOW Library of Crystallographic Prototypes (hereafter AFLOW Prototype Encyclopedia or Prototype Encyclopedia for brevity) [22], [23] has been designed with these objectives in mind. Integrated with the AFLOW computational framework, it can provide structural input for a wide variety of materials computational programs, including VASP [24], Quantum ESPRESSO[25], FHI-AIMS [26], ABINIT [27], and ELK [28] as well as in CIF format. Each structure's web page provides all the necessary crystallographic information, including space group, lattice vectors, and Wyckoff positions. In addition, the formulas for the primitive vectors and basis vectors of the structure are shown. This is particularly useful for students and novice researchers, as it shows the relationship between the standard crystallographic coordinates needed for computational work and the Cartesian positions of the atom in the primitive and/or conventional unit cell. If the desired chemical composition for the structure is not the prototype, the chemistry and primitive cell dimensions can be changed by the user before generating the structural input. Finally, the structure may be viewed as a primitive cell, conventional cell, or supercell at a variety of angles and magnifications via JSmol [29].

This article is about the ongoing development of the AFLOW Prototype Encyclopedia. In Part 1 [22], we introduced the Prototype Encyclopedia, which began as an updated version of the now-defunct Naval Research Laboratory “Structure of Crystals” web site. This was a collection of crystal structures that we found useful as a starting point for computational studies of materials. One feature of the site was that it included a number of well-known Strukturbericht designations, from the German effort to classify common crystal structures [4]. This article also provided a brief introduction of the crystallography needed to understand crystal structures, as well as a description of the entries in the AFLOW Prototype Encyclopedia for each structure. In all, 288 structures were included in the initial Prototype Encyclopedia.

Part 2 [23] continued the discussion of crystallography by reviewing the enantiomorphic space groups, which are pairs of space groups that are mirror images of each other. As part of our teaching mission, we also described the Wigner-Seitz version of the primitive unit cell of a crystal, and discussed the 17 two-dimensional “plane groups,” the analog of the 230 three-dimensional space groups. Another 302 structures were added to the database to bring the total to 590, with at least one structure shown in each of the 230 space groups.

In this article, Part 3, we add 510 new structures to the encyclopedia. These include all of the inorganic Strukturbericht designations which had not previously been cataloged by us. The Strukturbericht classification scheme was one of the earliest attempts to group elements¹ and compounds into common crystal structures. However, despite its historical importance there is no available history of its development, and until now there has been no comprehensive index of all the Strukturbericht designations that were defined in the series or added by others.

Recently, M. J. Mehl published a brief history of the development of the Strukturbericht designations [31]. In Part 3, we improve and extend that work, beginning with the introduction of these labels by Ewald [2] through the publication of the seven Strukturbericht volumes and the post-World War II extensions to the scheme made by Smithells [8], Pearson [5], and others. The Strukturbericht classifications changed over the run of the series, and several structures were published under multiple designations. Here, we track all of those changes.

The article is organized as follows: in Sections 2 and 3, we present common prototype classification schemes, followed by a short history of the development and presentation of Strukturbericht designations. As the Strukturbericht designations changed over time, Section 4 discusses the history of the major categories and sub-categories, as well as our editorial decisions as to which label should be used for a given prototype. Section 5 presents what we believe to be the first comprehensive list of Strukturbericht designations for elements and inorganic compounds, including all references to labels which we could find in the literature, with a link to the corresponding online pages in the AFLOW Prototype Encyclopedia. Section 6 describes AFLOW software modules that will be used to identify and classify new prototypes for future iterations of this work. Additionally, Section 7 introduces an online form for users to suggest new prototypes to enrich the Encyclopedia. Section 8 provides information about AFLOW Schools: hands-on workshops for students and researchers to learn about structural analysis methods — especially those discussed in Parts 1, 2, and 3 of this work — as well as other topics related to computational materials science. Section 9 summarizes our conclusions. This is followed by a list of all 510 new prototypes we have included in the Prototype Encyclopedia since the publication of Part 2.