Resolving competing distortions in Ca0.4Sr0.6TiO3 using complementary electron and X-ray techniques

Technical Summary: Resolving Competing Distortions in Ca₀.₄Sr₀.₆TiO₃

Problem Statement
The perovskite solid solution CaₓSr₁₋ₓTiO₃ exhibits complex, composition-dependent displacive phase transitions. While the phase diagram for x < 0.5 is generally accepted, significant contradictions remain regarding the structural nature of the high-temperature tetragonal $I4/mcm$ phase. Specifically, X-ray diffraction (XRD) data consistently indicate a tetragonal symmetry, whereas Raman spectroscopy measurements unequivocally suggest lower, orthorhombic symmetry. Previous attempts to reconcile these findings have proposed the existence of local, nanoscale structures with lower symmetry, but these features have not been directly observed. This study focuses on the composition Ca₀.₄Sr₀.₆TiO₃ to resolve the discrepancy between diffraction and spectroscopy data by investigating the structural evolution across the phase transition from the low-temperature orthorhombic $Pbcm$ phase to the high-temperature tetragonal $I4/mcm$ phase.

Methodology
The authors employed a complementary approach combining high-resolution synchrotron powder X-ray diffraction (PXRD) and variable-temperature transmission electron microscopy (TEM) with electron diffraction (ED).

• PXRD: Data were collected at the Diamond Light Source (beamline I11) over a temperature range of 100 K to 500 K. Rietveld refinements were performed using a symmetry-adapted basis derived from irreducible representations (irreps) of the cubic aristotype ($Pm\bar{3}m$). This allowed for the precise extraction of order parameters (OPs) associated with specific distortion modes ($T_2$, $\Delta_5$, $R_5^-$, $M_5^-$).
• TEM/ED: In-situ heating and cooling experiments were conducted on Ca₀.₄Sr₀.₆TiO₃ specimens. The study utilized selected area electron diffraction (SAED) and dark-field (DF) imaging. Crucially, DF images were generated using specific superstructure reflections corresponding to distinct distortion modes (e.g., $\Delta$-point for $k=(0,0,1/4)$ and $M$-point for $k=(1/2,1/2,0)$). This technique allowed for the direct visualization of microstructures associated with specific order parameters, complementing the average structural information provided by PXRD.

Key Results

1. Low-Temperature $Pbcm$ Structure: At room temperature and below, the material adopts an orthorhombic $Pbcm$ structure ($a^-a^-c^{++--}$). This phase is characterized by a combination of primary order parameters: $R_5^-$ (antiphase octahedral tilts) and $T_2$ (pairwise out-of-phase tilting along the c-axis). Secondary modes, including antiferrodistortive (AFD) displacements ($\Delta_5$) and a second-order Jahn-Teller (SOJT) distortion ($M_5^-$), are also present. In this phase, $M$-point superstructure reflections arise from the $M_5^-$ SOJT distortion of TiO₆ octahedra, not from in-phase octahedral rotations.
2. Microstructural Anisotropy: DF TEM imaging revealed that the coherence of the $T_2$ mode is limited along the c-axis ($[001]_{PC}$), resulting in a microstructure of thin nanoscale platelets separated by anti-phase boundaries. In contrast, the $R_5^-$ mode remains robust. This anisotropy is driven by the energy cost of reversing the tilt sequence, which is lower for boundaries perpendicular to the c-axis.
3. Phase Transition Dynamics: As temperature increases, the $T_2$ and $\Delta_5$ modes compete. Above 330 K, PXRD indicates a phase separation involving the $Pbcm$ phase and an intermediate $Cmcm$ phase before transitioning to the $I4/mcm$ phase above 380 K.
4. The High-Temperature Discrepancy Resolved:
   • PXRD: Above 380 K, PXRD patterns show only $R$-point reflections, consistent with a pure $I4/mcm$ phase ($a^0a^0c^-$) containing only out-of-phase tilts.
   • TEM/ED: Electron diffraction patterns, however, reveal the persistence of $M$-point superstructure reflections well above the transition temperature.
   • Imaging: DF images using $M$-point reflections show that the high-temperature phase contains a high density of nanoscale platelets (a few unit cells thick) exhibiting in-phase tilting ($M_2^+$). These platelets are too small to be detected by PXRD due to Scherrer broadening and the weak intensity of the associated peaks, but they are readily visible in electron microscopy due to the stronger interaction of electrons with matter. The presence of these in-phase tilts in the nanoscale regions explains the $M$-point reflections observed in the high-temperature phase, distinct from the $M_5^-$ SOJT mechanism active in the low-temperature phase.

Significance and Claims
The paper claims to resolve the long-standing discrepancy between Raman spectroscopy and diffraction measurements in Ca₀.₄Sr₀.₆TiO₃. The authors propose that the "lower symmetry" signals detected by Raman spectroscopy arise from the local structure of these nanoscale platelets, which possess in-phase tilts incompatible with the macroscopic $I4/mcm$ symmetry. These features persist well above the nominal phase transition temperature.

The study attributes the formation of this complex microstructure to the steep dependence of the phase transition temperature on composition ($dT_{C2}/dx \approx 1400$ K) combined with inevitable statistical fluctuations in composition at the atomic scale. This leads to local regions where different tilt systems coexist. The authors further suggest that this nanoscale microstructure explains other secondary effects, such as the hysteresis in phase transition temperatures and the softening of elastic constants observed in previous studies. By demonstrating how complementary electron and X-ray techniques can reveal hidden nanoscale order, the work provides a mechanism for understanding similar discrepancies in other compound perovskite oxide systems.