Over the recent decade, functional electronic materials design and discovery have shifted way from chemical-intuition-based towards data-driven synthesis and simulation. Numerous machine learning models have been developed to successfully predict materials properties and generate new crystal structures. Most existing approaches, however, rely much upon physical insights to construct handcrafted features (descriptors), which are not always readily available. For novel materials with sparse prior data and insufficient physical understanding, conventional machine learning models display limited predictability. In this talk, I will address this challenge by introducing an adaptive optimization engine for materials composition optimization, where feature engineering is not explicitly required. I then describe a use case where multi-objective Bayesian optimization with latent-variable Gaussian processes is utilized to accelerate the design of electronic metal-insulator transition compounds. Next, I will present a quantitative study on the structure-property relationship in crystal systems enabled by deep neural networks. The model which learns the structural genome could identify intrinsically similar structures in Fourier space. Finally I propose that these two methods could work harmoniously with each other towards an iterative exploration of novel functional materials.

That X-rays can affect the structure, and therefore functionality, of materials is well established. In macromolecular crystallography,

the phenomenology of ‘radiation damage’ is a mature and important field.[1] Conversely, discussions about radiation damage in small molecule crystallography are rarer and only starting to be identified.[2] X-ray-induced effects are somewhat less well studied in conventional inorganic systems, despite being implicated in a number of interesting phenomena. Examples include decomposition, conductivity enhancement, colour changes, spin-crossover, charge transfer, cell-parameter changes, crystallisation, and amorphisation.[3–5]

Cadmium cyanide, Cd(CN) ₂, is a flexible coordination polymer best studied for its strong and isotropic negative thermal expansion (NTE) effect. In this talk I will show that this NTE is actually X-ray exposure dependent: Cd(CN) ₂ contracts not only on heating but also on irradiation by X-rays.[6]

This behaviour contrasts that observed in other beam-sensitive materials, for which X-ray exposure drives lattice expansion. We call this effect ‘negative X-ray expansion’ (NXE) and suggest its origin involves an interaction between X-rays and cyanide ‘flips’; in particular, we rule out local heating as a possible mechanism.[7] Irradiation also affects the nature of a low-temperature phase

transition. Our analysis resolves discrepancies in NTE coefficients reported previously on the basis of X-ray diffraction measurements, and we establish the ‘true’ NTE behaviour of Cd(CN) ₂ across the temperature range 150–750 K. The interplay between irradiation and mechanical response in Cd(CN)₂ highlights the potential for exploiting X-ray exposure in the design of functional materials.

[1] E. F. Garman (2010) Acta Cryst. D 66, 339–351.

[2] J. Christensen, P. N. Horton, C. S. Bury, J. L. Dickerson, H. Taberman, E. F. Garman and S. J. Coles (2019) IUCrJ, 6, 703–713

[3] V. Kiryukhin, D. Casa, J. P. Hill, B. Keimer, A. Vigliante, Y. Tomioka and Y. Tokura (1997), Nature, 386, 813–815.

[4] H. Ishibashi, T. Y. Koo, Y. S. Hor, A. Borissov, P. G. Radaelli, Y. Horibe, S.-W. Cheong and V. Kiryukhin (2002), Phys. Rev. B

66, 144424

[5] M. Tu et al., (2021) Nat. Mater. 20, 93–99

[6] C. S. Coates, C. A. Murray, H. L. B. Boström, E. M. Reynolds and A. L. Goodwin (2021) Mater. Horiz.

The crystal chemistry of A^IB^IIXO₄ (A^I = Alkali ion, B^II = alkali-earth ion, X = P, V, As) is very rich and has been widely investigated, particularly the phosphate family [1]. In recent years, we have been investigated the crystal structures [2,3] and magnetic properties of some compositions within the A^IB^IIXO₄ series [4]. Besides the pure interest from a crystal chemistry point of view, the research activity related to this series of materials is driven mainly due to their ferroelectric, ferroelastic properties and possible applications as phosphors for LEDs [1, 5]. Within the rich A^IB^IIVO₄ sub-family (X = V), we have recently found a new structural type: the larnite structure with the composition NaSrVO₄ [3]. In this contribution, we are investigating its counter phosphate composition.

Despite its simple chemistry NaSrPO₄ has never been reported so far. Here, we present the synthesis, crystal structure and phase transitions of this phosphate. Surprisingly, this material exhibits a complex structure (31 atoms in the asymmetric unit-cell, Z = 10) at room temperature characterized by a strongly under bonded Na atom. This under-bonded atom is responsible for the complex and rich phase diagram as function of temperature as illustrated in Fig. 1. NaSrPO₄ exhibits 4 phase transitions between room temperature and 750°C. Besides its rich phase diagram, NaSrPO₄ exhibits a re-entrant phase transition slightly below 600°C before to reach a hexagonal paraelastic phase at high temperature. In addition, we show that the sequence of phase transitions is strongly driven by the history of the sample and several phases can be quenched at room temperature. Finally, the co-existence of Na channels within the structure with weakly bounded Na atoms makes this material a likely candidate for ionic conductivity.

[1] Isupov, V. A., (2002). Ferroelectrics 274, 203.

[2] Nénert, G., O’Meara, P. , Degen, T. (2017). Phys. Chem. Minerals 44, 455.

[3] Nénert, G., (2017). Z. Kristallogr. 232, 669.

[4] Nénert, G., et al. (2013). Inorg. Chem. 52, 9627.

[5] Choi, S., Yun, Y. J. , Kim, S. J., Jung, H.-K. (2013) Opt. Lett. 38, 1346.

Sr₂TiO₄, first member of the Ruddlesden-Popper series Sr_n+1Ti_nO_3n+1, has been long known to undergo a phase transition at 1550 °C. This transition makes the growth of single crystals of this material highly challenging, because it usually breaks the crystal into a periodic array of uneven lamellae. While the low temperature tetragonal phase is widely studied due to its close connection to the famous perovskite SrTiO₃, there is little information about the high temperature α-phase, except for an unindexed powder pattern by Drys&Trzebiatowski [1].

We stabilized the high-temperature α-Sr₂TiO₄ crystals by rapid cooling of the incongruent melt from above the liquidus temperature. The α-phase crystallizes in the orthorhombic Pna2₁ group with lattice parameters a=14.2901(5) Å b=5.8729(2) Å c=10.0872(3) Å and is isostructural to the orthorhombic forms of Sr₂VO₄ and Sr₂CrO₄ (which belong to the β-K₂SO₄ structure type). Its structure is formed by a complicated framework of large SrO_x polyhedra with tetrahedral cavities occupied by the transition metal. The tetrahedral coordination of Ti^IV makes the α-Sr₂TiO₄ quite a rare case among titanate compounds, the only other known example being the barium orthotitanate Ba₂TiO₄ [2].

However, whereas in Ba₂TiO₄ the coordination is tetrahedral in both high- and low-temperature polymorphs and the topotactic relation between the two is known, in the case of Sr₂TiO₄ a transition occurs to the layered Ruddlesden-Popper structure with octahedral titanium coordination.

In this work, we report for the first time the crystal structure of the high-temperature α-phase of Sr₂TiO₄. We elucidate the structural differences between the related compounds and discuss possible mechanism driving the structural transition.

[1] Drys, M., Trzebiatowski, W. (1957). Roczniki Chemii. 31, 489.

[2] Gunter, J., Jameson, G. (1984). Acta Cryst. C40, 207.

Magneto-caloric materials offer the possibility to design environmentally friendlier thermal management devices compared to the widely used gas-based systems [1]. These materials exhibit a change in entropy (ΔS_M) or a temperature change (ΔT_ad) when subjected to a magnetic field under isothermal or adiabatic conditions, respectively. The magnitude of change is largest about the materials Curie temperature (T_c) due to the order-disorder phase transition of the magnetic moments within the system. A suitable material must present a large magneto-caloric effect over a broad temperature span together with suitable secondary application parameters such as low heat capacity and high thermal conductivity. MnZnSb is derived from the PbFCl structure (in which the Mn sites are arranged within two-dimensional square nets), resulting in a pseudo 2D itinerant ferromagnetism which orders just above room temperature.

The first structural study reports that MnZnSb crystallises in the same anti-PbFCl-type structure as Mn₂Sb, with the tetragonal space group P4/nmm [2]. However, results from our experiments suggests that the true structure is more complex than this and has some aperiodic nature. Electron diffraction, in-house X-ray diffraction (Fig. 1(b)) and D20 neutron diffraction (Fig. 1(c)) data on powder samples all suggest that there is a small distortion of the tetragonal cell to a triclinic subgroup cell. As well as this, there appears to be incommensurate modulations in atomic positions and possibly Mn-Zn occupation (which is only seen in the neutron data). In the variable temperature neutron diffraction, we have also uncovered an unreported structural transition at ~130 K.

We have investigated the magneto-caloric properties of MnZnSb [3] using a combination of computational and experimental methods, including samples in which some Mn is substituted with Fe and Cr. Scaling analysis of the magnetic properties determines that they are second order phase transition ferromagnets and neutron diffraction has determined that the magnetic entropy change (Fig. 1(a)) is driven by the coupling of magneto-elastic strain in the square net through the magnetic transition. The primary and secondary application related properties have been measured experimentally, and the c/a parameter is identified as an accurate proxy to control the magnetic transition. Chemical substitution on the square net affords tuning of the Curie temperature over a broad temperature span between 252 and 322 K.

The epsilon phase of Fe₂O₃ (ε-Fe₂O₃, its least known polymorph) has gained considerable interest due to its intriguing properties and great application potentials. In the last few years this rare polymorph has received extraordinary attention due to its unique physical properties: it stands out for its huge coercive field (up to 2 T at room temperature), millimeter-wave ferromagnetic resonance, magneto-electric coupling, room temperature ferroelectricity, non-linear magneto-optical effect and photocatalytic activity [1-4].

ε-Fe₂O₃ presents a complex noncentrosymmetric structure (Pna2₁) with four distinct Fe sublattices: two positions in distorted octahedra (Fe1 and Fe2), one in regular octahedral environment (Fe3r), and one in distorted tetrahedral sites (Fe4t). This work examines the structural and magnetic phase transitions in ε-Fe₂O₃ nanoparticles (~20 nm) combining synchrotron X-ray and neutron diffraction measurements in the range 2-900 K. Complemented with X-ray absorption spectroscopy (XAS) and angle-dispersive X-ray diffraction under pressure up to 34 GPa.

The origin of the spin frustration was studied in the context of the rich magnetic phase diagram (with four different successive magnetic states) and its relationship with the magnetostructural transitions observed as a function of temperature. The successive magnetic transitions have been thoroughly studied in the whole temperature range, and have been fully described using the magnetic space groups approach. We have found that the spin frustration at the Fe³⁺ tetrahedral-site (Fe4t) not only is responsible for the unexpected different FIM1 (soft) and FIM2 (super-hard) commensurate ferrimagnetic phases [5], but also it is at the origin of the singular FIM2-to-ICM magnetic phase transition that disrupts the super-hard ferrimagnetic state of Pna'2₁' magnetic symmetry.

The structural evolution of ε-Fe₂O₃ is investigated across the magnetic transitions, putting the emphasis on the FIM1 (soft) to FIM2 (super-hard) phase transition. The observed coupling between structural and magnetic features explains the changes in the magnetic structures associated to the soft and super-hard phases. Puzzling changes are also observed between 150 and 100K, at the commensurate-incommensurate magnetic phase transition (FIM2-ICM) under cooling. The spiral magnetic structure previously proposed below 100 K does not match our neutron diffraction data. Incommensurate (ICM) collinear solutions compatible with neutron data are presented. This transition reduces the coercivity of ε-Fe₂O₃ (from 20 kOe to 0.8 kOe) and its ICM magnetic order (ground state) involves the formation of magnetic antiphase boundaries.

Finally, we report a polar-nonpolar structural phase transition under pressure associated to the volume collapse reported in [6]. The symmetry changes induced by pressure are fully described. The implications of this new centrosymmetric structure for understanding the mechanisms that allow the switching of the ferroelectric polarization in ε-Fe₂O₃ thin films are also analyzed.

[1] Namai, A.; Yoshikiyo, M.; Yamada, K.; Sakurai, S.; Goto, et al. (2012). Nature Commun. 3, 1035.

[2] Gich, M.; Fina, I.; Morelli, A.; Sánchez, F.; Alexe, M.; Gàzquez, J.; Fontcuberta, J.; Roig, A. (2014). Advanced Materials, 26, 4645.

[3] Xu, K.; Feng, J. S.; Liu, Z. P.; Xiang, H. J. (2018,). Physical Review Applied 9, 044011.

[4] X. Guan, L. Yao, K. Z. Rushchanskii, S. Inkinen, R. Yu, M. Ležaić, F. Sánchez, M. Gich, et al. (2020). Adv. Electron. Mater. 6, 1901134.

[5] García-Muñoz, J. L.; Romaguera, A.; Fauth, F.; Nogués, J. & Gich, M. (2017). Chemistry of Materials 29 (22), 9705.

[6] Sans, J. A., Monteseguro, V. et al. (2018). Nature Communications 9, 4554.

Keywords: ε-Fe₂O₃ , multiferroics, magnetic structures, magnetostructural coupling, nanoparticles

We acknowledge financial support from the European Research Council (ERC) under the EU Horizon 2020 programme (grant agreement No. [819623]). Also from the Spanish Ministerio de Ciencia, Innovación y Universidades (MINCIU), through Project No. RTI2018-098537-B-C21, cofunded by ERDF from EU, “Severo Ochoa” Programme for Centres of Excellence in R&D (FUNFUTURE (CEX2019-000917-S)) and MALTA Team network (RED2018-102612-T). We also acknowledge ILL and ALBA synchrotron for provision of beam time.

Simple solids such as TaS₂, NbSe₂, and CdI₂ show surprisingly complex polytypic behaviour where a number of crystalline structures can form whose unit cells differ only along their c-axis [1, 2]. This phenomena arises due to the differences in stacking sequences of the AB₂ layers along the c-axis. Although models have been developed to explain the complex phase behaviour, no model thus far has been able to account for all polytypes formed in practice [3, 4].

In this study we look at a new way of describing the structure of layered AB₂ compounds. Focusing on the layered dichalcogenides, we translate their structural degrees of freedom to a 1D model of coupled Ising chains to explain the polytypic behaviour. Our analysis suggests a family of ten ‘simplest’ ground states (Figure 1), seven of which have previously been reported. Using Monte Carlo simulations, we find that other phases identified in the literature but not expected by our model, are either describable as disordered states intermediate to our limiting phases, or mischaracterised. We proceed to show that the coupled 1D Ising chains encapsulate the behaviour of solid solutions of layered AB₂ systems, with a long term aim to link the properties of these materials to the interaction parameters relevant to the model. This phase control is an important result as it could lead to targeted design for specific properties, as structure is known to have a profound influence on materials’ properties.