Apparent Scarcity of Low-Density Polymorphs of Inorganic Solids

Abstract

For most inorganic solids, very few dense polymorphs and no low-density polymorphs are observed. Taking a wide range of tetrahedrally-coordinated binary solids (e.g., ZnO, GaN) as a prototypical system, we show that the apparent scarcity of low-density polymorphs is not due to significant structural or energetic limitations. Using databases of periodic networks as sources of novel crystal structures, followed by ab initio energy minimization, we predict a dense spectrum of low-density low-energy polymorphs. The diverse range of materials considered indicates that this is likely to be a general phenomenon. DOI: 10.1103/PhysRevLett.104.175503 PACS numbers: 61.50.Ah, 61.66.Fn, 71.15.Nc, 82.75.Fq The structure and properties of inorganic solids are intimately linked to such an extent that even different structures of the same composition (so-called polymorphs) often have widely differing properties and applications. For boron nitride (BN), for example, the soft hexagonal layered polymorph (h-BN) is used as a lubricant, while the cubic polymorph (wurtzite structure) is extremely hard and is employed as an industrial abrasive. Germanium also exhibits more than one polymorph (or more strictly ''allotrope'' for elemental systems) having very different optical properties; with the diamond structured -germanium having an indirect band gap, and the recently synthesized lowdensity clathrate-II structure [1] a direct gap. Evidently, having access to more than one polymorph can significantly extend the range of properties and applications of a particular compound. For the vast majority of inorganic solids, however, typically only three or fewer distinct polymorphs have been prepared experimentally and a similarly small number of hypothetical polymorphs have been proposed. Moreover, where more than one polymorph is known, these extra phases very rarely have a significantly lower density than the most stable polymorph.In stark contrast to this situation, silica (SiO 2 ) has been prepared as more than 40 polymorphs [2], the majority of which are considerably less dense than -quartz; the most stable polymorph under ambient conditions. The rich polymorphism of silica, especially in its low-density forms, allows for fine-tuning of applications (e.g., gas separation membranes) by choosing the best suited polymorph. In addition, 100 000þ hypothetical silica polymorphs have been predicted theoretically as fourfold-connected networks (4CNs) [3][4][5][6][7], a large fraction of which, after accurate theoretical evaluation as silica materials, were found to have comparable energetics to experimentally prepared polymorphs [8,9]. Similarly rich polymorphism has only been further observed for a select group of other inorganic solids, for example, aluminophosphates (AlPO 4 ). A tantalizing hint that there may as yet exist a greater pool of experimentally accessible polymorphs for many other inorganic solids is given by the recent low temperature deposition synthesis of the tetrahedral wurtzite polymorph of LiBr [10] (after previous theor...

The thermodynamic scale of inorganic crystalline metastability

“…It appears that the magnitude of the energy scale of metastability is similar to the strength of thermodynamic handles, suggesting that metastable structure-selection may be thermodynamic in origin, rather than kinetic. Furthermore, if the synthesis of metastable phases requires them to be stable under only some thermodynamic condition, perhaps there are no thermodynamic conditions under which our hypothetical, unobserved phases ( 12 , 16 ) are ever the lowest free-energy phases (dashed line, Fig. 3C).…”

Shedding Light on Structure–Property Relationships for Conjugated Microporous Polymers: The Importance of Rings and Strain

“…7,13,14 If this picture is true, then CMPs, CTFs, PAFs, and their like, would be the closest organic polymer analogues of well-known inorganic materials such as boron nitride, zinc oxide, and (alumino)silicates, materials whose structures are also based on 3- or 4-connected networks. 15−17 Alternatively, however, these materials could also resemble highly branched polymers or dendrimers, which are tree-like molecules with a relatively large number of end-groups but, typically, no closed rings. Structural hypotheses and models 14 aside, it is essentially unknown if CMPs, CTFs, and PAFs can be best described as highly branched polymers or as extended networks, or even as small but insoluble oligomers, which might nonetheless exhibit permanent microporosity.…”

Synthesis of an open-framework allotrope of silicon

“…However, low-pressure methods such as chemical vapour deposition could potentially enable larger scale production of Si 24 , as is the case for diamond 37 , another highpressure phase. Furthermore, the unique zeolite-like nature of this structure provides another perspective for synthesizing new lowdensity polymorphs in other classes of materials 38 , which would be of interest for gas and/or lithium storage and for molecularscale filtering applications 39 . More broadly, Si 24 expands the known allotropy in element fourteen and the novel high-pressure precursor synthesis approach suggests the potential for entirely new materials with desirable properties.…”