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Dawn Bonnell coauthored a quantitative analysis of piezoresponse force microscopy on ferroelectric surfaces. A signal from a biased probe can contain both electrostatic forces and a genuine electromechanical response; the observed contrast does not uniquely identify one mechanism. The analysis combines tip-field calculations and contact mechanics to map regimes where different contributions dominate. Comparing these predictions with temperature-dependent barium titanate domain measurements helps determine when the microscope can report material properties quantitatively.^[ref]

A researcher who coauthored measurements of electrical and optical properties of single-domain barium titanate crystals. The work compared dielectric response, spontaneous polarization, refractive index and birefringence as temperature changed. Relating these measurements to crystal preparation helped distinguish intrinsic material behavior from differences introduced by the growth method.^[ref]

A researcher who coauthored a study of the dielectric and optical response of barium titanate. Single-domain samples made it possible to relate spontaneous polarization and optical measurements to a controlled crystal state. Comparing growth methods showed how shifted phase transition temperatures can explain apparent differences between samples, an important issue when using crystals in optical devices.^[ref]

For identical thicknesses, compare $d/\kappa$ using the supplied coefficients:for barium titanate, lead zirconate titanate and quartz respectively. Thus barium titanate, then lead zirconate titanate, then quartz is the increasing voltage sensitivity of a piezoelectric sensor order. A large charge coefficient alone does not guarantee a large voltage: the large permittivity of a ferroelectric also increases its capacitance.

ferroelectric poling is essential. An initially unpoled ceramic has differently oriented crystal grains and domains whose charge responses largely cancel. An applied electric field favours suitably oriented domains and leaves a remanent macroscopic polarization after removal; it does not rotate all crystal grains into a single crystal.

In the linear coefficient model the added source polarization isThis is the stress-generated contribution at fixed electric field, equivalent to the short-circuit charge per face area. Under open-circuit conditions the induced field supplies an opposing dielectric contribution, so $\Delta D=0$; the source quantity must not be confused with a change of total free electrode charge. For scale, room-temperature single-domain barium titanate has spontaneous polarization of order $0.26\mathrm{C}{\mathrm{m}}^{-2}$: the calculated increment is about $3.0\times 10^{-4}$ of that value, a small response rather than wholesale reversal of the spontaneous polarization.^[ref]

For the requested displacement estimate, assign the whole additional dipole moment of one cell to movement of its single $\mathrm{T}{\mathrm{i}}^{4+}$ ion relative to a fixed background. Then $\Delta P=(4e)\Delta x/(a^{2}c)$, givingThis formal-charge estimate is only an equivalent displacement: real polarization changes involve oxygen and barium displacements, electronic polarization and Born effective charges, as well as possible domain-wall motion. The coefficient supplied for the ceramic cannot uniquely determine an actual microscopic titanium trajectory.

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.

A researcher who studied the electrical and optical properties of ferroelectric crystals. With collaborators, Wemple measured barium titanate's dielectric response and spontaneous polarization alongside optical absorption and birefringence. Comparing these observables across temperature connected the crystal's electrical ordering with its interaction with light.^[ref]