Apparent Scarcity of Low-Density Polymorphs of Inorganic Solids

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.

Figure 1

Structures of selected low-energy hypothetical TBSs: (a) 59_4_280312 ($3\mathrm{kJ}/\mathrm{mol}$), (b) 64_1_1 ($5\mathrm{kJ}/\mathrm{mol}$), (c) 189_3_1615 ($8\mathrm{kJ}/\mathrm{mol}$), (d) ATV ($13\mathrm{kJ}/\mathrm{mol}$), (e) SOD ($13\mathrm{kJ}/\mathrm{mol}$), (f) ATN ($17\mathrm{kJ}/\mathrm{mol}$). (a), (b), and (c) are based upon 4CNs from the database of Treacy et al. [1, 4, 38] and (d), (e), and (f) are derived from 4CNs known for porous crystalline silicates (i.e., zeolites) [15]. Energies in parentheses correspond to the energy difference of the ZnO form of the polymorph with respect to wurtzite-ZnO. The unit cell is boxed in each case.

Figure 2

Energies with respect to the wurtzite structure ($\Delta E_{\mathrm{wurtzite}}$) of a range of TBSs based on monovalent ions (a), divalent ions (b), trivalent ions (c), and tetravalent ions (d), plotted against their relative molecular volume ($V_m/V_{m\mathrm{wurtzite}}$). Points corresponding to previously predicted TBSs (Refs. [17, 18, 19, 20, 21]) are circled by dashed lines, while doped experimental TBSs are circled in black (Refs. [36, 37]).

Figure 3

Energy differences between the SOD and wurtzite polymorphs ($\Delta E_{\mathrm{SOD}\mathrm{\text{−}}\mathrm{wurtzite}}$) for a range of TBSs plotted against the absolute formal charges of the constituent ions. To highlight the generality of the observed correlation, points for other TBSs are also included (CuCl, BeO, AlN, AlP).