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An oxide with a perovskite structure. Near room temperature its tetragonal phase has switchable electric polarization and is ferroelectric. Its higher-temperature cubic phase is paraelectric.

An ideal cubic perovskite structure is obtained by putting La at the cube corners, Re at the body center, and N at the face centers. In fractional crystal coordinates one convenient basis isThe counting is $8/8=1$ La, one Re and $6/2=3$ N per cell. Corner-sharing $\mathrm{Re}{\mathrm{N}}_6$ octahedra form the network, with La in the larger interstices. The ideal cell illustrates the connectivity; octahedral tilting can lower the actual crystal symmetry.

Barium titanate has a high-temperature cubic perovskite structure, with Ti centred in its oxygen octahedron on average. This phase is paraelectric. Near room temperature the structure is tetragonal, with relative ionic displacements that give a spontaneous electric polarization. This phase is ferroelectric: an applied electric field can switch between differently polarized domains. Both phases have the same composition, BaTiO${}_3$; the transition near $120{}^{\circ }\mathrm{C}$ changes crystal symmetry and electrical response.

friction force microscopy records cantilever torsion caused by lateral tip–sample force. Choose the detector sign so that friction on a flat region contributes positively during a left-to-right trace. On a common laboratory-position axis, write the two signals schematically asHere $B$ is an offset and $G$ represents a slope-related lateral-force or detector cross-talk contribution. A reversed electronic convention reverses all plotted signs without changing the physical conclusions.

At the same controlled normal contact force $N$, the flat-region contribution is approximately $F_f=\mu N$. The lower perovskite structure plateaux give a larger trace–retrace separation than the upper inorganic surface, because their coefficient of kinetic friction is larger. Genuine friction reverses sign with scan direction, so a larger friction magnitude means a higher positive trace and a more negative retrace in this convention.

Sloped edges produce additional peaks or shoulders. The normal reaction to a slope has a lateral component, and the finite tip flank can contact the rim, so edge contrast is not a direct map of the local friction coefficient. With the two scans registered and load control maintained,The half-difference therefore emphasizes friction while the half-sum diagnoses common geometrical contributions. Real contact mechanics and imperfect registration can prevent exact cancellation. The bottom panel of the figure shows these two kinds of contrast separately.

The recorded profile has approximately 30 nm deep, flat-bottomed depressions with broadened, sloping edges. The full-height regions are the inorganic surface; the lower plateaux are the infiltrated perovskite structure. With adequate feedback control, imaging trace and retrace should agree when plotted against the same laboratory position.

The tip has a finite opening angle. Its flank contacts a pore rim before its apex can follow an ideal vertical wall, so tip convolution makes a narrow depression appear narrower and its sidewall less steep. For a flank angle $\alpha$ measured from the vertical, the horizontal distance needed to descend a height $h$ is $h\tan \alpha$. Along the cantilever, the nominal front and back values giveThus the two edges can have different apparent slopes. Across the cantilever, the nominal side angle instead gives about $12.4$ nm on each side. The scan orientation relative to the cantilever must therefore be specified before choosing the relevant pair of slopes.

Even a 100 nm wide pore leaves ample room for the tip apex to reach a flat bottom: in the along-cantilever idealization its bottom plateau is about $100-14-8=78$ nm wide. A 200 nm pore gives about 178 nm. The tip height is far greater than the 30 nm step, so it does not prevent access. An unreported finite apex radius adds edge rounding; its size cannot be inferred from the listed flank angles.