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Atomic Force Microscopy01:08

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Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid
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An analytic model for accurate spring constant calibration of rectangular atomic force microscope cantilevers.

Rui Li1,2, Hongfei Ye1, Weisheng Zhang1

  • 1State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China.

Scientific Reports
|October 30, 2015
PubMed
Summary

Accurate atomic force microscope (AFM) cantilever spring constant calibration is improved using thin plate theory. This new model reveals 3D and Poisson effects are crucial for precise force measurements.

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Area of Science:

  • Physics
  • Materials Science
  • Nanotechnology

Background:

  • Accurate force quantification in Atomic Force Microscopy (AFM) relies on precise spring constant calibration of the cantilever.
  • Existing methods often use beam theory, which has limitations in accuracy and scope.
  • Thin plate theory offers potential for higher accuracy but presents analytical challenges.

Purpose of the Study:

  • To develop an accurate analytical model for the static behavior of rectangular AFM cantilevers based on thin plate theory.
  • To investigate the influence of three-dimensional and Poisson effects on spring constant determination.
  • To establish a quantitative scaling law for normalized spring constants.

Main Methods:

  • Implementation of thin plate theory-based analytic modeling for rectangular AFM cantilevers.
  • Analysis of static behavior considering 3D and Poisson effects.
  • Validation using existing literature data and a refined finite element model.

Main Results:

  • Thin plate theory reveals significant roles of 3D and Poisson effects in spring constant calibration.
  • A quantitative scaling law was derived: normalized spring constant depends on Poisson's ratio, normalized dimension, and normalized load coordinate.
  • The model's predictions were validated against literature and finite element analysis.

Conclusions:

  • The developed thin plate theory model provides a more accurate method for AFM cantilever spring constant calibration.
  • The findings highlight the importance of considering 3D and Poisson effects for precise force measurements.
  • This model is expected to serve as a benchmark for future AFM cantilever calibration standards.