Scanning Nanomechanics

K.J. Wahl,¹ S.A. Syed Asif,² and R.J. Colton¹
¹Chemistry Division
²Present address: Hysitron, Inc.

Introduction: The invention of the scanning tunneling microscope (STM) and atomic force microscope (AFM) in the 1980s has led to rapid commercialization of microscopes that image surfaces with atomic resolution. As a result, our materials analyses capabilities at the nanoscale have expanded enormously and now include magnetic, dielectric, tribological, electrochemical, thermal, and mechanical properties. However, despite the many advances in commercially available instrumentation, dynamic mechanical analysis at this scale has been an elusive goal. To resolve this problem, we have developed a hybrid nanoindentation system capable of measuring quantitatively dynamic materials properties. The output of this instrument can also be in the form of an image or map of mechanical response or property (e.g., stiffness, modulus). This article describes NRL's recent advances in mapping dynamic mechanical properties.

Method: High-resolution mapping of mechanical properties is possible through the use of a "hybrid" nanoindenter that combines depth-sensing nanoindentation with an AFM. This combination enables quantitative nanomechanical properties analyses with nanometer-scale positioning and topographical mapping. These scanning and positioning capabilities allow investigations of materials and structures (e.g., composites, nanostructured materials, lithographic patterns, or micro-electromechanical systems (MEMS)) that have features below the optical limit.

In an indentation experiment, mechanical properties are evaluated by using a rigid probe of welldefined shape (e.g., a pyramid or sphere) to elastically or plastically deform a sample while monitoring the load and displacement response. We have improved the sensitivity of the hybrid nanoindenter by introducing a small sinusoidal component to the indentation force and detecting the displacement signal with a lock-in amplifier.¹ The result is a dynamic measurement of contact stiffness that is related to both the contact size and elastic properties of the contacting materials.

Two significant capabilities arise from these dynamic stiffness measurements. First, by scanning the sample under the oscillating probe at low loads (elastically), a two-dimensional map of the dynamic stiffness of the sample can be obtained.² Second, by varying the frequency of the oscillations, we can investigate dynamic mechanical properties inherent in many polymers and biomaterials. Figure 4 is a schematic of the instrument.

FIGURE 4
"Hybrid" scanning nanoindenter..The load-displacement response of a probe attached to a movable plate is actuated electrostatically to apply force; the displacement response is monitored by capacitive techniques.Sample x-y positioning and scanning are accomplished through a piezo-tube scanner.

Modulus Mapping of a Composite Material: Figure 5(a) shows a 10 X 10 mm image mapping the elastic (storage) modulus of a carbon fiberepoxy composite. Contrast in the image, as well as the rendered height, correspond directly to modulus with lighter regions having higher modulus. Figure 5 was obtained by applying a Hertzian contact model, describing the contact of a sphere against a flat, to the measured contact stiffness during the dynamic imaging of the composite. When the probe radius R, applied load P, and measured contact stiffness K are known, the reduced elastic modulus E* can be directly calculated, pixel by pixel, from the contact stiffness image data obtained during scanning:

Figure 5(b) shows a cross section through the center of the image of the elastic modulus. The image shows that the center of the carbon fiber has a lower modulus than the periphery, while the epoxy has a substantially lower modulus than the fiber.

FIGURE 5
(a) Two-dimensional map of the elastic modulus of a carbon fiber-epoxy composite material. Brighter regions of the image correspond to higher modulus. (b) Cross-section line scan through the center of the image (marked by arrows in (a)) shows the storage modulus in the epoxy and the modulus gradient at the center of the fiber.

The elastic modulus values obtained during the modulus mapping experiment were consistent with measured values from standard indentation experiments. More importantly, the low loads used during modulus mapping minimized the contact area between the probe and sample, thereby increasing the lateral resolution of the technique.

Imaging the Frequency-Dependent Properties of Polymers: Stiffness images can be acquired over a range of frequencies up to ~250 Hz, allowing investigation of dynamic mechanical properties of viscoelastic materials. Figure 6(a) and (b) shows two contact stiffness images of a cross section of a layered polystyrene (PS) sample, with alternating low (PS1) and high (PS2) molecular weights. The lighter regions in the images correspond to higher contact stiffness. The two images were taken from the same region of the sample while oscillating the probe at 105 and 200 Hz, respectively. At 200 Hz, the image contrast is reversed, indicating a strong frequency-dependent response of the two PS materials within this frequency range.

FIGURE 6
Stiffness images of alternating layers of polystyrene (PS) of two molecular weights at (a) 105 Hz and (b) 200 Hz. The contrast is due to frequency-dependent mechanical response of the polymers. The probe-sample response (1/stiffness) as a function of frequency shown in (c) is consistent with the stiffness images.

This image contrast reversal reflects a change in contact stiffness caused by the frequency-dependent dissipative properties of the two polymers. Figure 6(c) plots the dynamic compliance (1/stiffness) of the nanoindenter probe in contact with the two polymers as a function of frequency. This plot shows that the stiffness of PS1 should be lower than PS2 at 105 Hz, but higher than PS2 at 200 Hz. Because the compliance maxima (and equivalent stiffness minima) of the polymers occur near 100 Hz for PS1 and near 200 Hz for PS2, dynamic imaging at these two frequencies results in a stiffness contrast reversal due to the change in relative compliance between the polymers.

Summary: We have demonstrated the quantitative mapping of dynamic contact stiffness and elastic modulus with submicron spatial resolution. This new "scanning nanomechanics" technique is capable of mapping elastic and visco-elastic response and is an ideal tool for multiphase materials, composites, polymers, and nanostructures.

Acknowledgments: S.A. Syed Asif thanks AFOSR for postdoctoral support. We thank Oden Warren (Hysitron, Inc.) for helpful discussions and Paul Armistead (NRL) and Sergei Manganov (Digital Instruments) for providing samples.

[Sponsored by ONR and AFOSR]

References
¹ S.A. Syed Asif, K.J. Wahl, and R.J. Colton, "Nanoindentation and Contact Stiffness Measurement Using Force Modulation with a Capacitive Load Displacement Transducer," Rev. Sci. Instrum. 70, 2408 (1999).
² S.A. Syed Asif, K.J. Wahl, R.J. Colton, and O.L. Warren, "Quantitative Imaging of Nanoscale Mechanical Properties Using Hybrid Nanoindentation and Force Modulation,?"J. Appl. Phys. 90, 1192 (2001).