Atomic-scale analysis of cation ordering in reduced calcium titanate

The phenomenon of cation ordering is closely related to certain physical properties of complex oxides, which necessitates the search of underlying structure-property relationship at atomic resolution. Here we study the superlattices within reduced calcium titanate single crystal micro-pillars, which are unexpected from the originally proposed atomic model. Bright and dark contrasts at alternating Ti double layers perpendicular to b axis are clearly observed, but show no signs in corresponding image simulations based on the proposed atomic model. The multi-dimensional chemical analyses at atomic resolution reveal periodic lower Ti concentrations at alternating Ti double layers perpendicular to b axis. The following in-situ heating experiment shows no phase transition at the reported Tc and temperature independence of the superlattices. The dimerization of the Ti-Ti bonds at neighboring double rutile-type chains within Ti puckered sheets are directly observed, which is found to be not disturbed by the cation ordering at alternating Ti double layers. The characterization of cation ordering of complex oxides from chemical and structural point of view at atomic resolution, and its reaction to temperature variations are important for further understanding their basic physical properties and exploiting potential applications.

The phenomenon of cation ordering is closely related to certain physical properties of complex oxides, which necessitates the search of underlying structure-property relationship at atomic resolution. Here we study the superlattices within reduced calcium titanate single crystal micro-pillars, which are unexpected from the originally proposed atomic model. Bright and dark contrasts at alternating Ti double layers perpendicular to b axis are clearly observed, but show no signs in corresponding image simulations based on the proposed atomic model. The multi-dimensional chemical analyses at atomic resolution reveal periodic lower Ti concentrations at alternating Ti double layers perpendicular to b axis. The following in-situ heating experiment shows no phase transition at the reported T c and temperature independence of the superlattices. The dimerization of the Ti-Ti bonds at neighboring double rutile-type chains within Ti puckered sheets are directly observed, which is found to be not disturbed by the cation ordering at alternating Ti double layers. The characterization of cation ordering of complex oxides from chemical and structural point of view at atomic resolution, and its reaction to temperature variations are important for further understanding their basic physical properties and exploiting potential applications.
The reduced alkali metal and alkaline earth metal titanium oxides show various electronic and magnetic properties, among which Li 1+x Ti 2-x O 4 is most notable for its relatively high T c (~13 K) 1 . In 2002, the stoichiometric spinel MgTi 2 O 4 was reported to go through a metal to insulator phase transition at 260 K 2 , and an unusual helical Ti-Ti dimerization was identified in MgTi 2 O 4 later on 3 . As the ternary reduced titanate formed by the most close alkali metal to Mg, CaTi 2 O 4 was first synthesized and structurally characterized in 1956 4 , and single crystals of CaTi 2 O 4 was successfully grown in 1998 5 . It is predicted that CaTi 2 O 4 might experience a structural transition at 650 K (T c ) based on the similar downward trend of magnetic susceptibility below T c 6 as compared to MgTi 2 O 4 7 . The phenomenon of cation ordering has been investigated in a wide range of complex oxides including exploring related physical properties (dielectric, ferroelectric, magnetic, and electronic response, etc.) 8 as well as finding the underlying structure-property relationships based on characterization of the superstructures. For example, the ordering of lithium ions and vacancies is found to be responsible for the monoclinic distortion and the stability of the layered Li x CoO 2 structure upon lithium deintercalation 9 ; the compressibilities of pseudobrookite-type MgTi 2 O 5 are reported to be highly dependent on the degrees of Mg-Ti ordering under high pressure conditions 10 .
Traditionally, the analysis of the superstructure including cation ordering mainly relies on reciprocal characterization techniques like X-ray, neutron or electron diffraction 11,12 . Direct observation and quantitative characterization of superstructures at atomic resolution become possible thanks to the development of aberration corrector facilitated transmission electron microscopes (TEM) 13,14 . In this work, direct observation of superstructure in reduced calcium titanate is realized, which is unexpected for single-phase CaTi 2 O 4 . Based on simultaneous spectroscopical and spatial characterizations of the superstructure at sub-angstrom resolution, the observed superstructure is attributed to cation ordering along b axis. The study of temperature dependence of cation ordering and the atomic structure of CaTi 2 O 4 as a whole across the expected T c , and the influence of cation ordering on Ti-Ti dimmerization would be helpful for further understanding related physical properties in CaTi 2 O 4 and other complex oxides.

Results and Discussion
CaTi 2 O 4 (space group: Bbmm) is composed of double-rutile chains of edge-sharing TiO 6 octahedra, which are joined together by additional edge-sharing forming puckered TiO 6 octahedra sheets perpendicular to the b axis. The neighboring sheets have mirror relations connected through corner-sharing. As a result, one-dimensional tunnels form extending along the c axis, where the calcium atoms are located, as shown in the upper inset of Fig. 1a. The lattice parameters of the orthorhombic unit cell are determined to be: a = 9.718 Å, b = 9.960 Å, c = 3.140 Å from single crystal X-ray diffraction data 5 . Figure 1a is scanning electron microscopy (SEM) image of specific CaTi 2 O 4 micro-pillar showing smooth surfaces, the longer edge of the pillar is along c axis. Pt film was deposited in the region labeled by a green box as protection layer during FIB thinning. With irradiation of a Ga probe, trenches were formed on both sides before the central thin piece was lifted out, as shown in Fig. 1b, and the final thin piece of electron transparency is presented in the lower inset of Fig. 1b. Two pieces perpendicular to a and c axes were prepared, respectively, using the same method. The piece with surfaces perpendicular to a axis was characterized first by HRTEM and STEM-HAADF techniques. Figure   The aberration-corrected HAADF image projected along [001] is obtained from the same sample, as presented in Fig. 2b, which clearly shows the Ca and Ti atomic columns at atomic resolution. The top inset is arranged in the same way as that in Fig. 2a, and the simulation of HAADF image (left) is carried out employing MACTEMPAS software. The simulated image shows slightly higher intensities of the Ti columns than the Ca columns, and uniform contrasts for continuous (010) double Ti planes, as indicated by the blue arrows. Superstructure comprised of faint lines at the (010) planes with period of 2b in the experimental HAADF image is labeled by short blue lines attached to the long white arrow on the left. The corresponding intensity line profile across five periods of the superstructure along b axis is presented as a red curve, and overlapped to the experimental HAADF image. Since the two Ti layers composed of the double-rutile chains (labeled by blue arrows) are very close to each other, their projected intensities sum up and give an overall intensity of about twice that of the neighboring Ca layers (labeled by yellow arrows), and the double Ti layers show alternating high-low intensity peaks, with the faint lines corresponding to those higher peaks.
On the other hand, the intensity line profiles at Ti double layers along a axis show no obvious periodic intensity variations (Supplementary Figure S1a  atomic layers. The blue box includes one puckered Ti double-layers (at the faint line) and the neighboring Ca layer, the corresponding atom ratio is measured to be 2.1114. The cyan box contains the same Ca layer and the puckered Ti double-layers (between faint lines) below, which gives an atom ratio of 2.0950. The yellow box region corresponds to one period of the superstructure with an atom ratio of 2.1046, which is very close to the average value of the above two. Although the absolute values of the measured atom concentrations might not be entirely reliable, the chemical analyses carried out at different areas give similar trend of elemental distributions. Thus, it can be concluded that the superstructure along b axis is mainly attributed to periodic Ti deficiencies within alternating puckered Ti double-layers.
With no signatures of other impurity dopants of lighter elements from EDS measurements, the possibility of substitution of Ti positions for lighter elements is precluded. Since the Ti/Ca atom ratio between the faint lines is slightly lower than that right at the faint lines, it is quite possible that Ti vacancies appear in alternating Ti double layers, which contributes to smaller average atomic number for those Ti layers with lower intensity in the HAADF image. Close inspection of the projected Ti-Ti bond lengths reveals no difference for the alternating puckered Ti double-layers. Thus, there should not be large amount of Ti vacancies, with possible collapse of the double rutile chains, appearing in the puckered Ti double-layers. Since the scattered intensity for HAADF imaging is proportional to projected sample thickness, the Ti vacancy rate is evaluated from intensity line profile across single atomic columns along b axis, which gives a value of 9.86% for Ti double layers including vacancies.
The dependence of the superstructure on temperature is also studied. Considering the suggested structural transition of CaTi 2 O 4 at ~650 K (377 °C, T c ) 6 , the same sample with surface normal along [001] is heated from 20 °C (room temperature) to 500 °C. Figure 4a-c shows HRTEM images of specific area at 20 °C, 400 °C and 500 °C, respectively. The upper insets with black background are corresponding SAED patterns, the (020) and (400) diffraction spots are labeled, and the (0k0) (k = ±1, ±3, ±5…) spots are circled out for clarity. The SAED pattern with white background is simulation along the same direction based on the original atomic model, where the (0k0) reflections are kinematically forbidden. The appearance of the (0k0) reflections in the experimental SAED patterns could be attributed to cation ordering in alternating Ti double-layers in the form of Ti vacancies.
As the temperature increases, the crystal lattices do not have obvious differences among different temperatures, and all of the corresponding SAED patterns clearly show (0k0) reflections, indicating the existence of superstructures. Thus, the Ti vacancy induced cation ordering in alternating Ti double layers seems to be very stable at variable temperature conditions, which is different from the case of superstructures in potassium tungsten bronze nanosheets, where the W vacancies become more uniformly distributed at higher temperature 15 . Moreover, the suggested phase transition at ~377 °C 6 does not happen in the current case. It is possible that the existence of cation ordering hinders the transition around T c , or the observed downward trend of magnetic susceptibility below T c is resulted from other factors rather than phase transition as the case of MgTi 2 O 4 .
As mentioned above, a helical dimerization pattern was reported in MgTi 2 O 4 , which would result in orbital ordering and the opening of a gap between the fully occupied and unoccupied states 3 . The existence of Ti-Ti dimmers in CaTi 2 O 4 was also proposed from indirect experimental proofs 6,16 . In the standard CaTi 2 O 4 atomic model, the Ti-Ti distances within double rutile-type chains are 3.135 Å and 3.140 Å, while the Ti-Ti distance between Ti atoms in neighboring double rutile-type chains within a puckered sheet is 2.784 Å 6 . Figure 4d shows the single crystal model of CaTi 2 O 4 projected along c (top) and b (bottom) axes. The orange and green lines indicate Ti-Ti bonds within a double rutile-type chain, and between two neighboring chains, respectively, and the two types of bonds are of similar length as observed from c axis projection. When projected along b axis, the Ti atoms labeled as 1, 2, 3 in the top model are found to be at different heights along c axis. Thus, the length of orange bonds in the top model is projected length of the actually bonds.
The green and orange arrows in Supplementary Figure S1a label lines of atoms used for intensity profiles in Supplementary Figure S1c, and the types of atoms corresponding to the intensity peaks are added on top of Supplementary Figure S1c for clarity. It is found that the green Ti bond lengths are slightly larger than the orange bonds, which are measured to be 2.717 Å (orange bonds) and 2.765 Å (green bonds), respectively. After taking the projected bond angles into consideration, the actual bond lengths are 3.139 Å (orange) and 2.765 Å (green), which are very close to the reported values. Moreover, the blue rectangles in Supplementary Figure S1c label Ti double layers including possible Ti vacancies, and the green double arrows are of the same length, indicating similar Ti-Ti bond length at alternating regular Ti double layers and layers including Ti vacancies in between. Thus, the dimerization in CaTi 2 O 4 micro-pillars is clearly verified, which is not obviously affected by the existence of cation ordering in alternating Ti double layers perpendicular to b axis.

Conclusion
CaTi 2 O 4 micro-pillar single crystals are successfully synthesized. While the CaTi 2 O 4 crystal projected along a axis has the same structure as the proposed atomic model, the same crystal projected along c axis shows superstructures of bright and dark contrasts at alternating Ti double layers perpendicular to b axis, which is unexpected from both HRTEM and HAADF image simulations based on the original atomic model. Further EDS chemical analyses at atomic resolution preclude the existence of lighter elements as dopants, and reveal lower Ti concentrations at Ti double layers between the faint lines. The following in-situ heating experiment shows no obvious phase transition at the expected T c , and the cation ordering related superstructure is found to be temperature independent. Moreover, the dimerization of Ti-Ti bonds is clearly observed, which is not affected by cation ordering as well. Study of cation ordering in CaTi 2 O 4 from chemical and structural point of view at atomic resolution provides valuable information for tuning of cation ordering in CaTi 2 O 4 and related complex oxides, and for further understanding of their related physical properties.

Methods
Single crystals of CaTi 2 O 4 under study were prepared by the molten salt flux method. Equi-molar quantities of Ti metal powder (>99%) and CaTiO 3 powder (>99%) were ground together with CaCl 2 powder on the surface to prevent oxidation of the reactants. The temperature was quickly raised to 1000 °C at 130 °C/h and kept at 1000 °C for 6 h, and then cooled to 700 °C at 0.5 °C/min. The resultants were washed by deionized water to remove CaCl 2 , and the suspension was sonicated to separate the leftover. The comparatively larger crystals at bottom were CaTi 2 O 4 16 .
The obtained CaTi 2 O 4 single crystals are mostly micro-pillars with length in the range of 50~500 μm. Small pieces along certain orientations are cut out from specific CaTi 2 O 4 micro-pillar and thinned by FEI Quanta 3D FEG focused ion beam (FIB) for TEM observation. The high-resolution transmission electron microscopy (HRTEM) images, and aberration-corrected high-angle annular-dark-field (HAADF) images were obtained using FEI Titan G 2 60-300 with a probe Cs corrector operating at 300 kV. With a C2 aperture of 70 μm, the corresponding convergence semi-angle was ~28.8°. The atomic spectroscopic analysis was carried out using FEI Titan ChemiSTEM operating at 200 kV with the detector super EDS energy resolution ≤130 ev/100 kcps. The in situ heating experiment was completed using DENSsolution-DH30-4M-JU double-tilt heating/biasing holder.