The discovery of new materials is hampered by the lack of efficient approaches to the exploration of both the large number of possible elemental compositions for such materials, and of the candidate structures at each composition1. For example, the discovery of inorganic extended solid structures has relied on knowledge of crystal chemistry coupled with time-consuming materials synthesis with systematically varied elemental ratios2,3. Computational methods have been developed to guide synthesis by predicting structures at specific compositions4,5,6 and predicting compositions for known crystal structures7,8, with notable successes9,10. However, the challenge of finding qualitatively new, experimentally realizable compounds, with crystal structures where the unit cell and the atom positions within it differ from known structures, remains for compositionally complex systems. Many valuable properties arise from substitution into known crystal structures, but materials discovery using this approach alone risks both missing best-in-class performance and attempting design with incomplete knowledge8,11. Here we report the experimental discovery of two structure types by computational identification of the region of a complex inorganic phase field that contains them. This is achieved by computing probe structures that capture the chemical and structural diversity of the system and whose energies can be ranked against combinations of currently known materials. Subsequent experimental exploration of the lowest-energy regions of the computed phase diagram affords two materials with previously unreported crystal structures featuring unusual structural motifs. This approach will accelerate the systematic discovery of new materials in complex compositional spaces by efficiently guiding synthesis and enhancing the predictive power of the computational tools through expansion of the knowledge base underpinning them.
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We thank EPSRC for funding under EP/N004884. M.J.R. is a Royal Society Research Professor. We thank the Materials Chemistry Consortium (EPSRC: EP/L000202) and the PRACE-3IP project (FP7 RI-312763) for provision of computer time on the ARCHER UK National Supercomputing Service, and the N8 consortium (EPSRC: EP/K000225/1) and the University of Liverpool for access to local high-performance computing resources. We thank ISIS and Diamond Light Source for provision of beamtime and C. Tang, C. Murray and D. Fortes for assistance on the I11 and HRPD instruments. We acknowledge use of Hartree Centre resources in this work; the STFC Hartree Centre is a collaborative research laboratory in association with IBM providing high-performance computing platforms funded by the UK’s investment in e-infrastructure. We thank R. Seshadri and T. A. Strom (Materials Research Laboratory and Department of Materials, University of California, Santa Barbara) for measurement of the phosphor quantum yield. We are also grateful to K. Dawson, from the Centre for Materials and Structures at the University of Liverpool, for sample preparation with the Focussed Ion Beam.
The authors declare no competing financial interests.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
a, The flowchart of the MC-EMMA method. b, Large cation modules used in the testing of the MC-EMMA method on the structure of YBa2Ca2Fe5O13. Left, top to bottom; Ba4O4, Ca4O4, Ca3YO4, CaY3O4 and Ca2Y2O4. Right, top to bottom; Y4O4, Y4,Ca2Y2, CaY3 and Ca3Y. c, Small cation modules used in MC-EMMA testing. Top to bottom; FeO2 and four rotational variants of FeO. d, Energies of all converged structures using FF from YBa2Ca2Fe5O13 in eV per atom relative to the lowest energy structure. e, The experimental structure of YBa2Ca2Fe5O13. f, The lowest energy structure found by MC-EMMA, viewed along the  direction. The correct stacking sequence is observed, with mixed Y/Ca modules, capturing the main large cation site disorder in the experimental structure. This test of the MC-EMMA method was performed using FFs only, with FF parameters previously used with EMMA on the same system19. g, The structures of Ca2Fe2O5 (top left, ref. 76), YBa2Fe3O8 (bottom left, ref. 77) and YBa2Ca2Fe5O13 (right, ref. 78) (ideal) overlaid with coloured blocks indicated the MC-EMMA modular description using modules from b with the corresponding colour.
a, The nine modules used for the Y-Ba-Ti-O diagram (Y = yellow, Ti = cyan, Ba = green and O = red). b, Compositions of probe structures in the Y-Ba-Ti-O phase field; filled colours indicate the energy from the convex hull (Ehull), as shown in c, the point highlighted by the white cross is the lowest energy composition, YTi2Ba3O8.5, which is also the only experimentally known quaternary. d, Eight smaller cation modules used for melilite probe structures, with composition Ga24O56+δ, δ = 0, 1, 2, 3, 4, 8, 12, 16 (top row, left, to bottom row, right). e,13 decorations of the larger cation module used for melilite probe structures, containing up to three elements: A (blue), A′ (yellow), A″ (green). The module set is constructed using the combinations [A = Ca, A′ = Y, A″ = Sr], [A = Sr, A′ = Y, A″ = Ca] and [A = Y, A′ = Ca, A″ = Sr] (giving 39 combinations). For each module in d and e, three variants were created by the translations [+0.5, 0, 0] and [0, +0.5, 0] and by rotation of 90° about the c axis (resulting in 32 small cation modules and 156 large cation modules). f, The energies of the probe structures calculated using MC-EMMA with melilite modules are plotted relative to the convex hull created with previously reported phases (Extended Data Fig. 3); the lowest-energy quinary is highlighted in green.
a, Compositions for perovskite-derived probe structures in the Y-Sr-Ca-Ga-O phase field: 25 compositions highlighted with red circles are selected from the 691 possible with the modules and cell size limits in the MC-EMMA search. Given the low experimental Y content and the absence of Y in the DFT model structures of phases I and II, we show computed convex hulls in the reduced SrO-CaO-Ga2O3 phase diagram (that is, the Y = 0 plane of the Y2O3-SrO-CaO-Ga2O3 phase diagram shown in Extended Data Fig. 4). b, The convex hull calculated using previously reported phases. Blue circles are phases calculated to be on the hull, red squares are phases with DFT energies above the hull. c, The computed convex hull including the two new phases discovered in this study, phase I (Sr2Ca3Ga6O14) and phase II (SrCa2Ga2O6), shown as green circles on the hull. d, Energy of probe structures relative to the new convex hull shown in c which includes the newly discovered phases I and II. The energies (in eV per formula unit, see colour scale at right) are plotted on the Ga = 0.5 slice of the Y2O3-SrO-CaO-Ga2O3 phase diagram with black points showing the compositions of the probe structures. The DFT calculated energies (in eV per formula unit) of the experimentally reported phases are: Ca2Ga2O5, −56.278, Ca5Ga6O14, −156.837; CaGa2O4, −43.540; CaGa4O7, −73.995; Sr10Ga6O19, −214.803; Sr3Ga2O6, −67.690; Sr3Ga4O9, −99.074; Sr4Ga2O7, −79.737; SrGa2O4, −43.254; Y3Ga5O12, −145.076; YGaO3, −38.055; Y2O3, −45.772; Ga2O3, −30.178; CaO, 12.806; SrO, −12.055; Sr2Ca3Ga6O14, −156.143; and SrCa2Ga2O6, −68.999.
a, Principal component analysis results of the PXRD patterns of the initial 34 compositions sampled, with the analysis performed in Highscore Plus22; five samples do not cluster (dark blue), with the remainder grouped into three clusters (black, green and cyan), with composition 1 (referenced in main text and Fig. 2) falling into the cyan cluster. b, Representative PXRD pattern from the non-clustered samples represented in a, with symbols indicating known phases in the pattern36,38,79. c, d, Ga = 0.5 (c) and Y = 0.0 (d) slices of the Y2O3-SrO-CaO-Ga2O3 quaternary diagram, with nominal compositions coloured as in a, calculated compositions shown in black open circles and EDX data from composition 1 shown in grey. e, Synchrotron PXRD data (PSD, λ = 0.825781 Å) of composition 1, using the final refined models for each new phase. Reflections from the new phases I (black, 73.4(1) wt%) and II (red, 26.6(1) wt%) are marked. The inset indicates the location of the most intense reflections not indexed to either of the new phases with §. f, Lebail fit to PXRD data of Eu0.032Sr0.348Ca0.852Ga0.768O2.4 (composition 4). Inset, EDX data (black), observed points (red), nominal composition. g, Excitation (blue, detection wavelength 611 nm) and photoluminescence emission spectra for composition 4, excited at 390 nm (black) and 460 nm (red).
a,  view of LaSrGa3O7 melilite15,26(left) and I (right). The difference between the Ca,Sr cation occupancy on either side of the Ga3O7 layers in I doubles the c parameter compared to melilite (Fig. 3g). b,  view of the Sr2+ sites in melilite (left) and I (right), showing the superposition in I of three- and four-connected tetrahedra in the pentagonal rings that coordinate Sr2+ from the two neighbouring Ga3O7 layers, in contrast to the identical ring orientations in melilite. c, Two Ga3O7 layers in I viewed along  with one layer of cations between them. d,  view of the octahedral Ca1 site (dark blue, left) and the five-coordinate Ca2 site (light blue, right) in I where the displacement of the two pentagons contrasts with the near-superposition of the coordinating rings in the strontium-containing chains. The contacts from the Ca1 site to the bridging oxides displace the two pentagons above and below it relative to each other. Both Ca2 sites also coordinate to a bridging oxide from each ring. The Ca2 sites lie over the shared edge of two rings in one layer and are displaced towards two of the tetrahedra away from the ring centroid in the second layer. Mixed La/Sr (dark green), Sr (light green), Ca1 (dark blue), Ca2 (light blue), Ga(brown) and O(red).
a–c, Room temperature Rietveld refinements of sample with nominal composition 2 (Y0.038Sr0.320Ca0.848Ga0.794O2.416) containing 87.59(7) wt% phase II using synchrotron X-ray powder diffraction (χ2 = 3.84) data (a) and using neutron powder diffraction data from 168° bank, χ2 = 1.59 (b) and from 90° bank, χ2 = 4.9 (c) with a combined χ2 = 3.55 with 418 parameters. Space group F1. a = 15.4538(1) Å, b = 15.4573(1) Å, c = 15.4621(1) Å, α = 89.9990(7)°, β = 89.9669(7)°, γ = 89.9847(7)°. d–g, SAED (d) and CBED (e–g) patterns at increasing camera length of II along . The absence of symmetry confirms the space group assignment.
a, Structural units within the anion-deficient A16O10 layer of II. The smaller Ca4O rectangles (red) have dimensions of 3.32 Å × 3.42 Å, while the larger anion vacancy centred (Ca/Ga)4 rectangles (black) are 4.76 Å × 4.60 Å. The light blue rhombus with 2 Ca and 2 Ca/Ga vertices is also marked. b, Relation between polyhedra in the B1 layer and the anion vacancies in the A16O10 layer. (Top,  direction; bottom,  direction.) The oxide at the centre of Ca4O is located above the octahedral Ga, while the tetrahedral Ga is formed by rotation of the four coordinating oxides out of the B1 plane coupled with its location below the anion vacancies at the centre of the (Ca/Ga)4 rectangle. The SrO7 unit is formed from one ordered oxygen from an octahedron in the B1 plane, two oxygens from rotationally disordered GaO4 tetrahedra, two oxygens from tetrahedra within the B1 plane and two oxygens from the mixed Ca/Ga environment in the A layers; one above and one below the B1 plane. Bottom, perpendicular view of B1 layer with adjacent A layers. c, Relation between the A16O10 and B2 layer structures. (Top,  direction; bottom,  direction.) The oxide occupying the B site vacancy in the B2 layer has two of the four A site cation neighbours (which form the rhombus shown in a) displaced away from it to form the Ca4O square, with the two Ca/Ga sites displacing below the A16O10 plane to coordinate to the oxide. Rotation of the B2 layer oxides out of the plane at the four neighbouring GaO4 tetrahedra reduces anion–anion repulsion with the oxide ion on the B site. Atoms coloured as follows: Ga (brown), Sr (green), Ca (light blue) and O (red).
a, b, Observed unit cell volumes for phase I (a) and phase II (b) over the composition range in the initial synthetic study.
a, The fully ordered model of I used for DFT calculations. The combination of the three distinct layers in II with their disordered occupancies produces several near-equivalent three-dimensional connectivities. b, The connectivity used in the DFT calculations. c, d, The two ordered models of II used to understand the disorder present in the Rietveld refined structure, with different choices of cation clusters around the B-site oxygen anions boxed and shown at higher magnification in f and g, respectively. e, The disordered cation cluster identified within II, surrounding each of the B-site oxygen anions, which can be understood in terms of f, the cluster when all four cations in the cluster are set to GaO4 with the associated oxygen positions, and g, the cluster when all four cations are set to CaO5 with the associated oxygen positions. Atoms coloured as follows: Ga (brown), Sr (green), Ca (light blue) and O (red).
a, b, Five-coordinate calcium sites in the most stable (a) and in the fourth most stable (b) probe structures in the low-energy region of the phase diagram. Ca–O distances of less than 2.5 Å are shown with bonds, the next largest Ca–O distance is shown with a dashed arrow. All distances are given in ångströms. c, Ca–O environments in the computed probe structures compared with the experimentally refined Ca–O environments in phase I and phase II. d, Frequency of occurrence of coordination numbers for each of the cation species in the Y-Sr-Ca-Ga-O phase field in the DFT-relaxed probe structures (shown for Ga, from n = 170 calculated structures) and in the FF converged structures generated using MC-EMMA (n = 194,912) using perovskite-derived modules (black) and melilite-derived modules (red). Bonds were counted as being in the coordination sphere if the M–O interaction contributed >5% of the nominal charge when calculating the bond valence sum of the central cation.
This file contains single crystal solution for phase I. (TXT 376 kb)
This file contains powder cif file for the refinement of composition 2 with phase II in P1 space group. (TXT 6373 kb)
This file contains powder cif file for the refinement of composition 2 with phase II in F432 space group. (TXT 7337 kb)
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Collins, C., Dyer, M., Pitcher, M. et al. Accelerated discovery of two crystal structure types in a complex inorganic phase field. Nature 546, 280–284 (2017). https://doi.org/10.1038/nature22374
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