Bifurcation, chaos, and scan instability in dynamic atomic force microscopy
- Research Directorate, NASA Langley Research Center, Hampton, Virginia 23681 (United States)
- NLS Analytics, LLC, 375 Dundee Road, Glencoe, Illinois 60022 (United States)
The dynamical motion at any point on the cantilever of an atomic force microscope can be expressed quite generally as a superposition of simple harmonic oscillators corresponding to the vibrational modes allowed by the cantilever shape. Central to the dynamical equations is the representation of the cantilever-sample interaction force as a polynomial expansion with coefficients that account for the interaction force “stiffness,” the cantilever-to-sample energy transfer, and the displacement amplitude of cantilever oscillation. Renormalization of the cantilever beam model shows that for a given cantilever drive frequency cantilever dynamics can be accurately represented by a single nonlinear mass-spring model with frequency-dependent stiffness and damping coefficients [S. A. Cantrell and J. H. Cantrell, J. Appl. Phys. 110, 094314 (2011)]. Application of the Melnikov method to the renormalized dynamical equation is shown to predict a cascade of period doubling bifurcations with increasing cantilever drive force that terminates in chaos. The threshold value of the drive force necessary to initiate bifurcation is shown to depend strongly on the cantilever setpoint and drive frequency, effective damping coefficient, nonlinearity of the cantilever-sample interaction force, and the displacement amplitude of cantilever oscillation. The model predicts the experimentally observed interruptions of the bifurcation cascade for cantilevers of sufficiently large stiffness. Operational factors leading to the loss of image quality in dynamic atomic force microscopy are addressed, and guidelines for optimizing scan stability are proposed using a quantitative analysis based on system dynamical parameters and choice of feedback loop parameter.
- OSTI ID:
- 22594533
- Journal Information:
- Journal of Applied Physics, Vol. 119, Issue 12; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-8979
- Country of Publication:
- United States
- Language:
- English
Similar Records
Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film-shape memory alloy composite cantilever plate subjected to in-plane harmonic and stochastic excitation
Bifurcations and chaos of a vibration isolation system with magneto-rheological damper
Related Subjects
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
AMPLITUDES
ATOMIC FORCE MICROSCOPY
BIFURCATION
CHAOS THEORY
DAMPING
ENERGY TRANSFER
EQUATIONS
FLEXIBILITY
FREQUENCY DEPENDENCE
HARMONIC OSCILLATORS
IMAGES
INSTABILITY
INTERACTIONS
NONLINEAR PROBLEMS
OPTIMIZATION
OSCILLATIONS
POLYNOMIALS
RENORMALIZATION