409 Atomic Force 17. Atomic Force Microscopy in Solid Mechanics Ioannis Chasiotis Scanning probe microscopes (SPMs) have become a key instrument for the application and sensing of nanonewton forces in small material volumes and the measurement of in-plane and out-of- plane strains with nanometer resolution. The versatility of SPMs lies with the ability to specify the nature of tip-material interaction forces in order to probe relevant nanoscale phenomena or control the position of individual atoms and molecules that is not possible by other high- resolution imaging instruments. As a result, new capabilities in nanoscale experimentation and mechanics of materials at the nanometer scale have emerged along with new challenges and opportunities for further developments. It is the objective of this chapter to introduce the new as well as the advanced SPM user to the underlying operating principles, the advantages, and the limitations of SPMs. 17.1 Tip–Sample Force Interactions in Scanning Force Microscopy ................ 411 17.2 Instrumentation for Atomic Force Microscopy ................... 412 17.2.1 AFM Cantilever and Tip .................. 414 17.2.2 Calibration of Cantilever Stiffness ... 415 17.2.3 Tip Imaging Artifacts ..................... 417 17.2.4 Piezoelectric Actuator ................... 419 17.2.5 PZT Actuator Nonlinearities ............ 420 17.3 Imaging Modes by an Atomic Force Microscope .............. 423 17.3.1 Contact AFM................................. 423 17.3.2 Non-Contact and Intermittent Contact AFM ........ 425 17.3.3 Phase Imaging ............................. 430 17.3.4 Atomic Resolution by an AFM ......... 431 17.4 Quantitative Measurements in Solid Mechanics with an AFM ............. 432 17.4.1 Force-Displacement Curves ............ 432 17.4.2 Full Field Strain Measurements by an AFM ................................... 434 17.5 Closing Remarks ................................... 438 17.6 Bibliography ........................................ 439 References .................................................. 440 The term scanning probe microscopy (SPM) engulfs methods that utilize force interactions or tunneling cur- rent flow between a probe and a surface to construct a mapping of the geometric and material properties of the sample surface. The two most common methods are scanning tunneling microscopy (STM) [17.1] and atomic force microscopy (AFM) [17.2] that use a sharp tip to measure the tunneling current and the tip–sample force interactions, respectively. The latter are either short range (quantum mechanical, electrostatic) or long range (van der Waals), such as magnetic and electro- static forces. Because the distance dependence of these forces is very strong, Angstrom-scale tip–sample sepa- rations can be detected and be translated into equivalent imaging resolution. Furthermore, local force interac- tions can be used for spectroscopic analyses: the spatial distribution of various forces may be employed to con- struct an image of the surface and potentially its spatial composition. Along the same lines, optical information can be obtained by using near-field scanning optical mi- croscopy (NSOM) [17.3, 4] that is built according to conventional AFM instrumentation. The spatial resolu- tion depends on the nature and magnitude of the forces describing the tip-surface interaction, and the geometry and size of the probe. A first step to increase the spa- tial, in-plane, resolution is to control the tip diameter that varies between 10–15 nm, and, in part, determines the interaction volume of the sample material. SPM has evolved significantly since its birth [17.1] because it provides capabilities that are complemen- Part B 17 Springer Handbook of Experimental Solid Mechanics Sharpe (Ed.) • ! Springer 2008 1