Anomalous structure transition in undercooled melt regulates polymorphic selection in barium titanate crystallization

The crystallization processes of titanates are central to the fabrication of optical and electrical crystals and glasses, but their rich polymorphism is not fully understood. Here, we show when and how polymorphic selection occurs during the crystallization of barium titanate (BaTiO3, BT) using in situ high energy synchrotron X-ray diffraction and ab initio molecular dynamic simulation. An anomalous structure transition is found in molten BT during cooling across the cubic-hexagonal transition temperature, which enables nucleation selection of BT by manipulating the undercooling: a cubic phase is preferred if nucleation is triggered at large undercooling, whereas a hexagonal phase is promoted at small undercooling. We further reveal that the nucleation selection between the cubic and the hexagonal phase is regulated by the intrinsic structure property of the melt, in particular, the degree of polymerization between Ti-O polyhedra. These findings provide an innovative perspective to link the polymorphic crystallization to the non-isomorphic structure transition of the melt beyond the conventional cognition of structural heredity.


Supplementary Note 1. Microstructure and phase compositions
Nucleation was triggered at a series of undercoolings and a multi-path crystallization behavior was observed. If triggered nucleation at small undercoolings (ΔT = 78.1 K and 177.9 K), both h-BT and t-BT were detected after solidification. On the contrary, if triggered nucleation at large undercoolings, only t-BT can be obtained. Analogous results were also reported by Yu et al 1 .
To clarify the origin of the polymorphic selection behavior of BT, microstructural analyses were carried out. Fig. S1(a)-(c) present the SEM images of three selected regions (top, middle and bottom) of a solidified sample. As shown in Fig. S1(a), a layer of fine equiaxed grains with a thickness of ~ 50 μm is observed near the top boundary of the sample. Below this boundary layer, grains become obviously large, and solidification defects (cracks or shrinkage cavity) are more commonly observed. The middle region of the sample mainly consists of coarse equiaxed crystals, as shown in Fig. S1(b). Near the triggering point at the bottom, columnar-like BT crystals are formed (Fig. S1(c)). These crystals are aligned in parallel with growth direction perpendicular to the sample boundary. 2 Formation of the above microstructure is illustrated by a schematic diagram (Fig. S1(d)).
At the quenching spot (bottom), the droplet contacts with the water-cooled nozzle directly.
Heat is conducted rapidly from the droplet to the nozzle in a direction perpendicular to the contact surface, which results in a preferential crystal growth along the direction of heat flow. On the top of the droplet, a local quenching zone appears due to the fastest cooling rate, which results from an uneven temperature distribution within the suspending droplet 2 . In this region, homogeneous nucleation and no-directional heat flow result in formation of fine equiaxial crystals. The middle part of the sample is the final solidified region due to release of latent heat of crystallization and the lowest heat transport rate.
Low nucleation rate facilitates the emergence of coarse equiaxial crystals. To identify the distribution of hexagonal and tetragonal phases, Raman mapping analysis is employed. h-BT and t-BT have distinct characteristic Raman peaks 3,4 , as shown in Fig. S2(a). The regional distribution of two phases in the above-mentioned three typical regions is presented in Fig. S2(b)-(d). At the top side of the sample, only h-BT is detected; on the contrary, only t-BT presents near the vicinity of the triggering point. In the middle of the sample, a hybrid phase distribution is observed, which has a distinct dividing line along the grain boundary. Combining the microstructure features and the regional distribution of two phases, we concluded that: i) both c-BT and h-BT nucleate from melt directly, rather than from a solid-state phase transition; ii) the undercooling before crystal nucleation of c-BT is larger than that of h-BT because the quenching effect of the water-cooled nozzle (triggering point) is much stronger than natural cooling (the top side). iii) The possibility of cross-nucleation in c-/h-BT selection is low, although it's very common in simpler condensed matter systems 5,6 , as these two phases present obvious regional distribution rather than coupled distribution.
Polymorphic selection in undercooled melt during solidification is often accompanied by a change in crystal morphology, as observed in RMnO3 (R = rare-earth element) 7 and our previous work 8 , which indicates different crystal growth modes of different phases.
However, such effect is not observed in BT.  intensity of the diffraction rings is reduced greatly and the feature of the melt is clear, which correspond to re-melting in the diffraction region due to release of latent heat. In 6 the late stage of solidification (t6, t8 and t10), more distinct diffraction spots are observed illustrating that the number of grains is reduced but the size is expanded during the remelting stage, which is consistent with the microstructure shown in Fig. S1(b).
Furthermore, comparing the integral diffraction patterns before re-melting (t3 and t4) with those after re-melting (t6-t12), it is found that the patterns resemble more to h-BT after re-melting, which demonstrates that part of c-BT disappears due to its lower thermal stability at the re-melting temperature (near melting point).
It should be pointed out that the collection time is much longer than the time scale of nucleation, but it is sufficient to determine whether the solid-state phase transition occurs during the crystallization process 9 . The real time HEXRD experiment proves that both h-BT and c-BT (perovskite) nucleate directly from undercooled melt. c-BT precipitates from the triggering point where the undercooling is large, and h-BT nucleates from the melt at the top side of the droplet where the undercooling is low. Therefore, coexistence of two phases within the sample triggered nucleation at a small undercooling is attributed to uneven temperature distribution and nucleation sequences manipulated by undercoolings.  various atmospheres (oxygen, air and nitrogen) and found that the density of CA melt decreased with increasing oxygen partial pressure 11 .Therefore, we re-measure the density of molten BT under our experimental condition. A schematic view of the experimental setup is given in Fig S7. For density measurement, the temperature-time profile was recorded, Fig S8(a). Realtime dimensional changes of the molten drops were captured by a high-speed camera.
The imaging acquisition frequency was set five times of the temperature recording frequency (50 per second). Therefore, five density values were obtained for each temperature. Average value and the associated error bar at a certain temperature are calculated from these five results.
The measured densities at various temperatures are presented in Fig. S8 The change of ρ-T relationship indicates that BT melt may go through a distinct structural or dynamic evolution when quenching from superheating state to undercooling state. Extrapolating the density of molten BT to room temperature yields a value of ~ 5.21 g cm -3 , which is very close to the density of BT amorphous film fabricated by radiofrequency plasma sputtering 12 .

Supplementary Note 4. Pair weighting factors W ij
The pair weighting factor Wij, showing the contribution to the total X-ray scattering intensity of each atomic pair in BT, is calculated using concentration of atoms and Xray atomic form factor of elements according to:  Differing from the initial AIMD simulation run, a re-run parallel AIMD simulation was performed from different starting configurations. The total simulation time of re-run 12 AIMD simulation was set 20 ps with timesteps of 2 fs, and the last 10 ps configurations was used to calculate the Ti-O coordination number (CNTiO). As shown in Fig. S10(a), the CNTiO results are slightly different from the initial AIMD running, but the overall trend are not changed. Most important is that the discontinuous CNTiO transition taking place between 1583 K and 1523 K is still robust, which is accordant with our finding and conclusion in manuscript. We must admit that both the new starting configuration and the initial starting configuration are generated by fitting our experimental structural functions through running Reverse Monte Carlo (RMC) simulation, and the total energy of two ensembles are quite approximate.
In order to further test the anomalous CNTiO transition, we construct a random starting configuration, in which we only ensure the atoms are not too close to each other (matching the cutoff radius) without fitting the experimental correlation functions. This random starting configuration was first relaxed at 3000 K for over 10 ps, and then quenched to transition temperatures (1583 K and 1523 K) for another 20 ps equilibration. As presented in Fig. S10(b), the random starting configurations correspond to a higher total energy even after AIMD simulation, which indicates that the ensembles originating from the random starting configurations are relatively metastable state compared with that from the initial starting configurations. We compared the CNTiO and found the transition was still existed, but the magnitude of CNTiO transition is just half of that determined by the initial starting configuration.
In summary, we believe and convince that the discontinuously anomalous structure transition exists in undercooled BT liquid. The conclusion is robust and can be reproduced by diffraction experiments as well as AIMD simulation. One important thing should be emphasized that the transition magnitude determined by AIMD may be closely related to the total energy state of starting configuration. A relatively stable (lower total energy) starting liquid configuration may be more helpful for studying this liquid-liquid structural transition.