Synthetic accessibility and stability rules of NASICONs

In this paper we develop the stability rules for NASICON-structured materials, as an example of compounds with complex bond topology and composition. By first-principles high-throughput computation of 3881 potential NASICON phases, we have developed guiding stability rules of NASICON and validated the ab initio predictive capability through the synthesis of six attempted materials, five of which were successful. A simple two-dimensional descriptor for predicting NASICON stability was extracted with sure independence screening and machine learned ranking, which classifies NASICON phases in terms of their synthetic accessibility. This machine-learned tolerance factor is based on the Na content, elemental radii and electronegativities, and the Madelung energy and can offer reasonable accuracy for separating stable and unstable NASICONs. This work will not only provide tools to understand the synthetic accessibility of NASICON-type materials, but also demonstrates an efficient paradigm for discovering new materials with complicated composition and atomic structure.

Proof That a Dominant Endmember Formula Can Always Be Written for a Mineral or a Crystal Structure

An endmember formula must be: (1) conformable with the crystal structure of the mineral, (2) electroneutral (i.e., not carry a net electric charge), and (3) irreducible [i.e., not capable of being factored into components that have the same bond topology (atomic arrangement) as that of the original formula]. The stoichiometry of an endmember formula must match the “stoichiometry” of the sites in the structure; for ease of expression, I denote such a formula here as a chemical endmember. In order for a chemical endmember to be a true endmember, the corresponding structure must obey the valence-sum rule of bond-valence theory. For most minerals, the chemical endmember and the (true) endmember are the same. However, where local order would lead to strong deviation from the valence-sum rule for some local arrangements, such arrangements cannot occur and the (true) endmember differs from the chemical endmember. I present heuristic and algebraic proofs that a specific chemical formula can always be represented by a corresponding dominant endmember formula. That dominant endmember may be derived by calculating the difference between the mineral formula considered and all of the possible endmember compositions; the endmember formula which is closest to the mineral formula considered is the dominant endmember.

Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Brute-force compute campaigns relying on demanding ab initio calculations routinely search for previously unknown materials in chemical compound space (CCS), the vast set of all conceivable stable combinations of elements and structural configurations. Here, we demonstrate that four-dimensional chirality arising from antisymmetry of alchemical perturbations dissects CCS and defines approximate ranks, which reduce its formal dimensionality and break down its combinatorial scaling. The resulting “alchemical” enantiomers have the same electronic energy up to the third order, independent of respective covalent bond topology, imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of CCS and enables the establishment of trends without empiricism for any materials with fixed lattices. We demonstrate the efficacy for three cases: (i) new rules for electronic energy contributions to chemical bonding; (ii) analysis of the electron density of BN-doped benzene; and (iii) ranking over 2000 and 4 million BN-doped naphthalene and picene derivatives, respectively.

Ontology, archetypes and the definition of ‘mineral species’

Ontology deals with questions concerning what things exist, and how such things may be associated according to similarities and differences and related within a hierarchy. Ontology provides a rigorous way to develop a general definition of a mineral species. Properties may be divided into two principal groups: an intrinsic property is characteristic of the object and is independent of anything else; an extrinsic property depends on the relation between the object and other things. A universal is an entity that is common to all objects in a set. Here the objects are mineral samples, each entity is a specific property of these minerals, and the set of objects is all mineral samples of that mineral species. The key intrinsic properties of a mineral species are its name, its end-member formula and Z (the number of formula units in the unit cell), its space group and the bond topology of the end-member structure. These are also universals as they are common to all mineral samples belonging to that mineral species. An archetype is a pure form which embodies the fundamental characteristics of an object. Thus the archetype of a mineral species embodies the above set of universals. Real mineral samples of this mineral species are imperfect copies of that archetype, with a range of chemical composition defined by the boundaries between end-member formulae of this and other end members of the same bond topology. The result is a formal definition of a mineral species: A specific mineral species is the set of imperfect copies of the corresponding archetype and is defined by the following set of universals: name, end-member formula and Z, space group, and bond topology of the end-member structure, with the range of chemical composition limited by the compositional boundaries between end members with the same bond topology.

Expanding the family of mineral-like anhydrous alkali copper sulfate framework structures: new phases, topological analysis and evaluation of ion migration potentialities

Two novel compounds, K2Cu3(SO4)4 and KNaCu(SO4)2, were synthesized. The crystal structure of K2Cu3(SO4)4 is based on a [Cu3(SO4)4]2− framework with relatively simple bond topology, but with four different CuO n polyhedron geometries. The K+ cations reside in the pores of the framework. The [Cu(SO4)2]2− framework in KNaCu(SO4)2 encloses large elliptical channels running along [001]. Larger channels are occupied by K+, whereas smaller ones are filled by Na+. The bond-valence energy landscape (BVEL) approach has been demonstrated to be a useful method for the prediction of the mobility of alkali metal ions in various structures. By means of this approach, the threshold energies at which isosurfaces begin to percolate as well as the directions of possible ion migration in the structures were determined. The modelling of ion migration maps by the analysis of the procrystal electron-density distribution was used to rapidly identify ion migration pathways and limiting barriers between particular crystallographic sites in the structures under consideration. Its consistency and complementarity with the BVEL method have been demonstrated. Both approaches revealed a relatively low ion threshold percolation and migration barriers in the cryptochalcite-type structures [cryptochalcite: K2Cu5O(SO4)5]. Hence, one may assume that its 3D framework type is suited for ion transport applications. The review of all known members of the groups of anhydrous copper sulfates did not reveal a correlation between the porosity of the framework structures and a manifestation of ion conduction properties.

Hydration in aqueous osmolyte solutions: the case of TMAO and urea

X-ray Raman scattering spectroscopy and first principles simulations reveal details of the hydration and hydrogen-bond topology of trimethylamine N-oxide (TMAO) and urea in aqueous solutions.

A priori bond-valence and bond-length calculations in rock-forming minerals

Within the framework of the bond-valence model, one may write equations describing the valence-sum rule and the loop rule in terms of the constituent bond valences. These are collectively called the network equations, and can be solved for a specific bond topology to calculate its a priori bond valences. A priori bond valences are the ideal values of bond strengths intrinsic to a given bond topology that depend strictly on the formal valences of the ion at each site in the structure, and the bond-topological characteristics of the structure (i.e. the ion connectivity). The a priori bond valences are calculated for selected rock-forming minerals, beginning with a simple example (magnesiochromite, = 1.379 bits per atom) and progressing through a series of gradually more complex minerals (grossular, diopside, forsterite, fluoro-phlogopite, phlogopite, fluoro-tremolite, tremolite, albite) to finish with epidote (= 4.187 bits per atom). The effects of weak bonds (hydrogen bonds, long Na+—O2− bonds) on the calculation of a priori bond valences and bond lengths are examined. For the selected set of minerals, a priori and observed bond valences and bond lengths scatter closely about the 1:1 line with an average deviation of 0.04 v.u. and 0.048 Å and maximum deviations of 0.16 v.u. and 0.620 Å. The scatter of the corresponding a priori and observed bond lengths is strongly a function of the Lewis acidity of the constituent cation. For cations of high Lewis acidity, the range of differences between the a priori and observed bond lengths is small, whereas for cations of low Lewis acidity, the range of differences between the a priori and observed bond lengths is large. These calculations allow assessment of the strain in a crystal structure and provide a way to examine the effect of bond topology on variation in observed bond lengths for the same ion-pair in different bond topologies.