Theory of indentation of piezoelectric materials

Giannakopoulos, A.E.; Suresh, S.

doi:10.1016/s1359-6454(99)00076-2

Cited by 273 publications

(137 citation statements)

References 14 publications

(11 reference statements)

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“…A rigorous mathematical description of the problem is extremely complex; fortunately, the geometry of the tip-surface junction in PFM is remarkably similar to the piezoelectric indentation problem. [53][54][55][56][57] In the classical limit, the coupled electromechanical problem is solved for mixed-value boundary conditions: V s ϭV tip in the contact area and the normal component of the electric field E z ϭ0 elsewhere. However, in the typical PFM experiment the contact area is small and deformation occurs even when the tip is not in contact due to the local electric field.…”

Section: Electromechanical Regimementioning

confidence: 99%

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Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces

2002

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In order to determine the origin of image contrast in piezoresponse force microscopy (PFM), analytical descriptions of the complex interactions between a small tip and ferroelectric surface are derived for several sets of limiting conditions. Image charge calculations are used to determine potential and field distributions at the tip-surface junction between a spherical tip and an anisotropic dielectric half plane. Methods of Hertzian mechanics are used to calculate the response amplitude in the electrostatic regime. In the electromechanical regime, the limits of strong (classical) and weak (field-induced) indentation are established and the relative contributions of electroelastic constants are determined. These results are used to construct ''piezoresponse contrast mechanism maps'' that correlate the imaging conditions with the PFM contrast mechanisms. Conditions for quantitative PFM imaging are set forth. Variable-temperature PFM imaging of domain structures in BaTiO 3 and the temperature dependence of the piezoresponse are compared with GinzburgDevonshire theory. An approach to the simultaneous acquisition of piezoresponse and surface potential images is proposed. In order to determine the origin of image contrast in piezoresponse force microscopy ͑PFM͒, analytical descriptions of the complex interactions between a small tip and ferroelectric surface are derived for several sets of limiting conditions. Image charge calculations are used to determine potential and field distributions at the tip-surface junction between a spherical tip and an anisotropic dielectric half plane. Methods of Hertzian mechanics are used to calculate the response amplitude in the electrostatic regime. In the electromechanical regime, the limits of strong ͑classical͒ and weak ͑field-induced͒ indentation are established and the relative contributions of electroelastic constants are determined. These results are used to construct ''piezoresponse contrast mechanism maps'' that correlate the imaging conditions with the PFM contrast mechanisms. Conditions for quantitative PFM imaging are set forth. Variable-temperature PFM imaging of domain structures in BaTiO 3 and the temperature dependence of the piezoresponse are compared with Ginzburg-Devonshire theory. An approach to the simultaneous acquisition of piezoresponse and surface potential images is proposed.

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Section: Electromechanical Regimementioning

confidence: 99%

“…A complete description of the strong-indentation limit is given by Giannakopoulos and Suresh, 55 who extended Hertzian contact mechanics to piezoelectric materials. The relationship between the load P, indentor potential V, and indentation depths h is…”

Section: A Strong Indentationmentioning

confidence: 99%

Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces

2002

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“…1(a)]. 17 In this classical, or strong indentation (SI) limit, piezoresponse becomes independent of tip geometry and can be calculated analytically in terms of materials properties. However, the SI limit does not apply to all situations.…”

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confidence: 99%

Contrast Mechanism Maps for Piezoresponse Force Microscopy

Kalinin

Bonnell

2002

J. Mater. Res.

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Piezoresponse force microscopy (PFM) is one of the most established techniques for the observation and local modification of ferroelectric domain structures on the submicron level. Both electrostatic and electromechanical interactions contribute at the tip-surface junction in a complex manner, which has resulted in multiple controversies in the interpretation of PFM. Here we analyze the influence of experimental conditions such as tip radius of curvature, indentation force, and cantilever stiffness on PFM image contrast. These results are used to construct contrast mechanism maps, which correlate the imaging conditions with the dominant contrast mechanisms. Conditions under which materials properties can be determined quantitatively are elucidated.

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“…In addition to the material response, the acquired image I ij is expected to contain noise, as well as certain additional non-stochastic variations which have no relation to the concerned phenomena. Such variation in I ij can occur due to (i) varying PFM tip-sample contact conditions, [45][46][47] and/or (ii) the presence of relative drifts between each image (columns of I ij ). The linear drift between the images is easily removed as a part of the preprocessing step (see supplementary material); however, removal of the non-linear drift is not always trivial.…”

Section: Introductionmentioning

confidence: 99%

Sequential piezoresponse force microscopy and the ‘small-data’ problem

et al. 2018

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The term big-data in the context of materials science not only stands for the volume, but also for the heterogeneous nature of the characterization data-sets. This is a common problem in combinatorial searches in materials science, as well as chemistry. However, these data-sets may well be 'small' in terms of limited step-size of the measurement variables. Due to this limitation, application of higher-order statistics is not effective, and the choice of a suitable unsupervised learning method is restricted to those utilizing lower-order statistics. As an interesting case study, we present here variable magnetic-field Piezoresponse Force Microscopy (PFM) study of composite multiferroics, where due to experimental limitations the magnetic field dependence of piezoresponse is registered with a coarse step-size. An efficient extraction of this dependence, which corresponds to the local magnetoelectric effect, forms the central problem of this work. We evaluate the performance of Principal Component Analysis (PCA) as a simple unsupervised learning technique, by pre-labeling possible patterns in the data using Density Based Clustering (DBSCAN). Based on this combinational analysis, we highlight how PCA using non-central second-moment can be useful in such cases for extracting information about the local material response and the corresponding spatial distribution.

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Theory of indentation of piezoelectric materials

Cited by 273 publications

References 14 publications

Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces

Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces

Contrast Mechanism Maps for Piezoresponse Force Microscopy

Sequential piezoresponse force microscopy and the ‘small-data’ problem

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