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Atomic force acoustic microscopy Influence of the lateral contact stiffness on the elastic measurements.pdf

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Atomic force acoustic microscopy Influence of the lateral contact stiffness on the elastic measurements.pdf

Ultrasonics 71 (2016) 271–277 Contents lists available at ScienceDirect Ultrasonics journal homepage: /locate/ultras Atomic force acoustic microscopy: In?uence of the lateral contact stiffness on the elastic measurements F.J. Flores-Ruiz a,b,?, F.J. Espinoza-Beltrán b, C.J. Diliegros-Godines a, J.M. Siqueiros a, A. Herrera-Gómez b a Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México, km. 107, Carretera Tijuana-Ensenada, 22860 Ensenada, B.C., Mexico b CINVESTAV Unidad Querétaro, Lib. Norponiente 2000, Real de Juriquilla, 76230 Querétaro, Qro., Mexico article info Article history: Received 12 May 2016 Received in revised form 6 July 2016 Accepted 8 July 2016 Available online 9 July 2016 Keywords: Acoustics Atomic force microscopy Beams Contact stiffness Flexural vibrations Ultrasonics Young’s modulus abstract Atomic force acoustic microscopy is a dynamic technique where the resonances of a cantilever, that has its tip in contact with the sample, are used to quantify local elastic properties of surfaces. Since the contact resonance frequencies (CRFs) monotonically increase with the tip-sample contact stiffness, they are used to evaluate the local elastic properties of the surfaces through a suitable contact mechanical model. The CRFs depends on both, normal and lateral contact stiffness, kN and kS respectively, where the last one is taken either as constant (kS 1), or as zero, leading to uncertainty in the estimation of the elastic properties of composite materials. In this work, resonance spectra for free and contact vibration were used in a ?nite element analysis of cantilevers to show the in?uence of kS in the resonance curves due to changes in the kS/kN ratio. These curves have regions for the different vibrational modes that are both, strongly and weakly dependent on kS, and they can be used in a selective manner to obtain a precise mapping of elastic properties. ó 2016 Published by Elsevier B.V. 1. Introduction Atomic force acoustic