High-throughput crystal structure solution using prototypes

Databases of density functional theory (DFT) calculations, such as the Open Quantum Materials Database (OQMD), have paved the way for accelerated materials discovery. DFT calculations require crystal structure information as input; however, due to inherent challenges in solving a compound's structure from powder diffraction data alone, there are thousands of experimentally synthesized compounds whose structures remain unsolved. We present a rapid DFT-based structure solution method capable of resolving numerous outstanding structure solution problems at low computational cost. The method involves (1) searching inorganic compound databases for all prototypes that match known structural characteristics of the compound, such as stoichiometry, space group, and number of atoms per cell, (2) performing DFT calculations of the target composition in each of the structural prototypes, and (3) evaluating these prototypes as candidates using a combination of DFT energy and match between calculated and experimental diffraction pattern. As this approach is straightforward and inexpensive, we employ it to solve 521 previously unsolved compounds from the Powder Diffraction File, resulting in a 1.4% expansion of the set of all experimental compounds in the OQMD. DFT calculations of these compounds could yield valuable properties.

Figure 1

Flow chart of the prototype searching method to solve structures. The compound $\mathrm{V}{\mathrm{I}}_3$ (PDF no. 00-023-0719) is presented here as an example. Using experimentally determined structure attributes absent atomic coordinates, we search the OQMD for all prototypes with the space group ($\mathrm{R}\overline{3}$), stoichiometry $\left(A{B}_3\right)$, and 6 formula units per cell. We then evaluate each of the three prototypes found ($\mathrm{Fe}{\mathrm{F}}_3$-type, $\mathrm{Pd}{\mathrm{F}}_3$-type, $\mathrm{Bi}{\mathrm{I}}_3$-type) using DFT and $R$ factor. We find that the $\mathrm{Bi}{\mathrm{I}}_3$ prototype is the most plausible solution because it has the lowest formation energy and $R$ factor.

Figure 2

Sorted numbers of compounds associated with prototypes in the 2011 version of the ICSD, present in the OQMD. The total number of compounds in this ICSD set is 36 807. The most prevalent (rank 1) prototype is $\mathrm{Th}{\mathrm{Cr}}_2{\mathrm{Si}}_2$, with 657 compounds in the ICSD; and the second-most prevalent (rank 2) prototype is ZrNiAl, with 466 compounds. Beginning at rank 10 or so, the trend in prototype prevalence smoothly decays with a wide tail.

Figure 3

Distribution of the number of (a) OQMD prototypes and (b) candidate structures matching stoichiometry, space group, and number of formula units per unit cell of 603 PDF entries with missing atomic coordinates.

Figure 4

DFT-computed 90th percentile convex hull distance (meV/atom) of ICSD compounds containing each element on the periodic table. The metastability of materials is chemistry dependent, with carbides and nitrides standing out as being particularly high in energy. Gray shaded elements are excluded from this analysis.

Figure 5

(a) Distribution of convex hull distances of 624 compounds with structures obtained by prototype searching in this work, compared to 23 247 ICSD compounds that have been calculated in the OQMD. Inset is the same distribution between 0 and 25 meV/atom; almost half of the 624 compounds lie within 5 meV/atom of the convex hull, somewhat shy of the ICSD. (b) Distribution of $R$ factors of 624 compounds with structures obtained by prototype searching in this work, compared to 136 randomly chosen solved compounds from the PDF. (c) Convex hull distances and $R$ factors of 624 compounds with structures obtained by prototype searching. Green pluses and red dots are compounds that passed and failed validation checks, respectively. (d) Discrepancies in the best-performing candidate structure energies and $R$ factors with the lowest-energy and lowest-R-factor candidate structures. Only cases with multiple candidate structures are shown (403 of 624 PDF compounds). The vast majority (91%) of cases lie within the shaded region; in other words, the best-performing candidate structure usually is close to the lowest energy and lowest $R$ factor of all candidate structures. Cases with low discrepancy are also more likely to pass our validation checks (84%) than cases with high discrepancy (59%).

Figure 6

The percentage of the prototypes chosen for each of 624 PDF compounds that pass our validation criteria, plotted against the chemical similarities $P$ of these compounds to ICSD compounds of the same prototype. The chemical similarities $P$ are binned by decades on a log scale; see the text of Sec. 3 for the definition of $P$ between a pair of compounds. The top, middle, and bottom plots focus on binary, ternary, and quaternary compounds, respectively. The numbers of compounds that fall within each range of chemical similarities are shown beside the data points. The trends demonstrate that compounds that pass our validation criteria are more likely to be chemically similar to ICSD compounds than compounds that fail.

Figure 7

151 of our solutions that pass validation criteria are metals (0 eV), 284 are semiconductors (0–4 eV), and 85 are insulators (≥4 eV); band gap was not determined for one solution.

Figure 8

Crystal structures of 9 of the 521 materials solved using prototypes. The compositions of the solved materials are in bold, and the prototypes are in parentheses. Note that some of the solutions presented here have the same prototype, specifically ${\mathrm{Ba}}_2\mathrm{Mo}{\mathrm{O}}_5$ and ${\mathrm{Rb}}_2\mathrm{Ga}{\mathrm{F}}_5$ as well as $\mathrm{LiFe}{\mathrm{O}}_2$, VO(OH), and CrO(OH).

Figure 9

(a) Diffraction pattern describing the prototype solution ${\mathrm{Ti}}_8{\mathrm{Bi}}_9$ for the compound ${\mathrm{Hf}}_8{\mathrm{Bi}}_9$ from the PDF (top), compared to the experimental XRD pattern reported in the PDF for ${\mathrm{Hf}}_8{\mathrm{Bi}}_9$ (bottom). The $R$ factor is 0.21, highlighting a close match between the two patterns. (b) “New” Hf-Bi convex hull including ${\mathrm{Hf}}_8{\mathrm{Bi}}_9$ solution generated from DFT calculations stored in the OQMD, plotted against the “old” convex hull found in the OQMD not including ${\mathrm{Hf}}_8{\mathrm{Bi}}_9$. Since our ${\mathrm{Hf}}_8{\mathrm{Bi}}_9$ solution was lower in energy by 46 meV/atom than the old convex hull at that composition, we construct a new convex hull to include our solution.