Gerold A. Schneider

Nanoscale reconstruction of surface crystallography from three-dimensional polarization distribution in ferroelectric barium–titanate ceramics

The three-dimensional orientation of polarization vectors at the surface of ferroelectric barium–titanate (BaTiO3) ceramics is evaluated using voltage-modulated scanning force microscopy (SFM). By applying an ac voltage to the conductive SFM tip, we measure the relative amount of the three orthogonal components Px, Py, and Pz, of the polarization vector at any surface point. The measured polarization orientation together with the actual domain-wall orientation allows a precise reconstruction of the crystallographic orientation of the investigated grains down to a 40 nm resolution. Excellent agreement is obtained when comparing this orientation with the crystallographic reconstruction revealed by etch patterns from the sample surface topography. We show that the surface topography manifests a domain structure, which was present in the past, while the actual ferroelectric domain configuration is revealed by the modulation technique.

A fracture criterion for conducting cracks in homogeneously poled piezoelectric PZT-PIC 151 ceramics

Abstract A fracture criterion for conducting cracks in piezoelectric ceramics under combined electrical and mechanical loads is proposed in connection with a measured material specific fracture curve of PZT-PIC 151. The characteristic fracture curve of the investigated material is a function of the stress intensity factor, K I , which is known from fracture mechanical concepts, and the recently defined electric field intensity factor, K E , for conducting cracks. A four-point-bending device for fracture tests under combined electrical and mechanical loads serves as the experimental set-up. The measured quantities, force, displacement, applied voltage and crack length, are used to evaluate the experiments. The finite element method (FEM) was used to determine the mechanical stress intensity factor, K I , and the electric field intensity factor, K E , taking into account linear piezoelectric coupling in the material. A qualitative process zone model is proposed for a physical interpretation of the fracture curve.

High-resolution characterization of piezoelectric ceramics by ultrasonic scanning force microscopy techniques

The local elastic properties and the ferroelectric domain configuration of piezoelectric ceramics have been examined by atomic force acoustic microscopy and by ultrasonic piezoelectric force microscopy. The contrast mechanisms of the two techniques are discussed. From the local contact stiffness which is obtained by evaluation of the contact resonance spectra, the elastic constants of the sample surface can be calculated. In the case of anisotropic materials these elastic constants correspond to the indentation moduli. Indentation moduli for barium titanate and for a lead zirconate-titanate ceramics were calculated theoretically and are in reasonable agreement with experiments. The non-linearity of the tip–sample interaction becomes noticeable at large vibration amplitudes or large mechanical tip loads.

R-curve behaviour of BaTiO3 due to stress-induced ferroelastic domain switching

Abstract R-curves of ferroelectric barium titanate have been measured with CT-specimens. Depending on the grain size, the R-curves exhibit an increase from an initial value of 0.5–0.7 MPa√m to a plateau value of 0.7–1.2 MPa√m after a crack length increment of approximately 100–800 μm. The main toughening mechanism is thought to be ferroelastic domain switching leading to the development of a process zone around the crack. The small differences in the initial values of the R-curves are attributed to grain bridging, crack deflection and crack branching associated with large grains. Applying an electric field perpendicular to the specimen plane results in an increased initial fracture toughness and a stronger R-curve behaviour. Time-dependent reorientation of domains in the crack wake causes stress relaxation combined with a strong time dependence of the R-curves. A qualitative process zone model is proposed to explain these effects.

Influence of the electric field on vickers indentation crack growth in BaTiO3

In this study, the Vickers indentation method was used to determine the crack growth of ferroelectric barium titanate (BaTiO3) ceramic under the influence of electric fields. It was verified that an applied electric field induces distinct anisotropic crack growth parallel and perpendicular to the poling direction which is mainly interpreted as an anisotropy in fracture toughness. The curve of the measured crack lengths as a function of the applied electric field shows similarity with the strain hysteresis. Curves of cracks parallel and perpendicular to the electric field direction are symmetric to each other. Stress-induced ferroelastic domain switching is used to explain the observed crack lengths anisotropy and change in fracture toughness.

Modeling and measurement of surface displacements in BaTiO3 bulk material in piezoresponse force microscopy

Piezoresponse force microscopy (PFM) is applied to image ferroelastic formed c domains in a single crystal ferroelectric barium titanate bulk material. A simple model and an analytical approach are presented, which provides a basis to understand the complex tip-surface interactions responsible for the image contrast in PFM. In particular, the measured amplitude of the piezoresponse out-of-plane surface displacements of a C− domain is compared with theoretical results based upon a three-dimensional Green’s function solution. The electric field distribution in the tip-surface contact is determined using image-charge calculations for a spherical tip separated by a thin water layer from a mechanically isotropic and electrically anisotropic dielectric half plane.

The fracture behaviour of dental enamel

Enamel is the hardest tissue in the human body covering the crowns of teeth. Whereas the underlying dental material dentin is very well characterized in terms of mechanical and fracture properties, available data for enamel are quite limited and are apart from the most recent investigation mainly based on indentation studies. Within the current study, stable crack-growth experiments in bovine enamel have been performed, to measure fracture resistance curves for enamel. Single edge notched bending specimens (SENB) prepared out of bovine incisors were tested in 3-point bending and subsequently analysed using optical and environmental scanning electron microscopy. Cracks propagated primarily within the protein-rich rod sheaths and crack propagation occurred under an inclined angle to initial notch direction not only due to enamel rod and hydroxyapatite crystallite orientation but potentially also due to protein shearing. Determined mode I fracture resistance curves ranged from 0.8-1.5 MPa*m(1/2) at the beginning of crack propagation up to 4.4 MPa*m(1/2) at 500 microm crack extension; corresponding mode II values ranged from 0.3 to 1.5 MPa*m(1/2).

The electrical potential difference across cracks in PZT measured by Kelvin Probe Microscopy and the implications for fracture

An indentation crack in a poled PZT ceramic subjected to an electric field is investigated using AFM and KFM to determine the crack opening displacement and the electrical potential difference across the crack. The experimental results are used to calculate the crack tip stress and dielectric displacement intensity factors and the crack tip energy release rate. From the applied electric field and the measured field interior to the crack, the dielectric constant of the crack interior is determined to be 40. The consequences of this permittivity on the crack tip energy release rate are illustrated for a Griffith crack. The theoretically predicted effect of an applied electric field in retarding crack growth decreases significantly with increasing permittivity. In practical situations in terms of crack length, applied load and electric field level, the retardation of crack growth is negligible when the dielectric constant of the crack interior is higher than 20.

Cyclic fatigue due to electric loading in ferroelectric ceramics

Abstract Mechanical fatigue of ferroelectric ceramics due to bipolar cyclic electric loading is examined. Beam specimens out of three different PZT materials were cut and precracks were initiated by Vickers indentation. The specimens were loaded by alternating electric fields varied from 0·9 to 1·0 and 1·5 times the coercive field Ec. In short intervals the crack propagation was measured. Before and after fatigue experiments electric polarisation and strain were measured as a function of the electric field. The crack growth rate decreases with increasing cycle number, and a saturation point is reached after approximately 105 cycles. A correlation between growth rates and ferroelectric strain was detected. Measured strain loops suggest that switching of ferroelectric domains undergoes a strong fatigue effect. Therefore after 106 cycles the elastic strain is not as strong a driving force for further crack extension. In addition fatigue-crack growth is strongly dependent on the material and the electric field strength.

Stress induced movement of ferroelastic domain walls in BaTiO3 single crystals evaluated by scanning force microscopy

Abstract We report on the quantitative investigation of lateral domain wall motion in BaTiO 3 single crystals subjected to a compressive unidirectional mechanical stress. Simultaneous to the mechanical testing, the single crystals prepared by the modified exaggerated growth method were characterized by scanning force microscopy and piezoresponse force microscopy (PFM) which allow both topographical details and the true three-dimensional ferroelectric domain configuration to be reproduced simultaneously. Stress induced domain formation is initiated at the sample surface followed by the forward- and lateral-domain growth both perpendicular and parallel to the direction of induced stress. Knowing the crystallographic orientation of the BaTiO 3 single crystal (from Kikuchi patterns) clearly associates our experimental observations with a 90° domain switching process, in accordance with a theoretical model. Additionally, 180° ferroelectric domain boundaries ( a -domains) were detected with PFM which are not visible from the sample topography. The formation of these newly formed domains is driven by the compensation of the positive surface charge arising from the ferroelastic growth of C + domains.