Glossary

Acoustic atomic force microscopy (AAFM) An implementation of SPM where the variation of the flexural resonance spectrum of an SPM cantilever as it is scanned over a sample surface is used to extract local mechanical properties from that surface.

Acoustic microscopy A nondestructive analytical technique whereby acoustic waves are transmitted or reflected from a material using acoustic lenses to elucidate mechanical properties, mass density, or acoustic properties of materials.

Atomic force microscopy (AFM) An implementation of SPM wherein the deflection of a cantilevered tip scanned over a sample surface is converted to a surface topography map, typically, with subnanometer out-of-plane resolution. Bending modulus (k) The second derivative of surface energy density with respect to curvature. For a tube, k = Ea/(1 — a2), where a is Poisson's ratio and a is the tube wall thickness.

Bulk modulus (B) Typically defined as the ratio of a hydrostatically applied pressure to the resulting fractional change in volume.

Cantilevered tip A pyramidal tip placed at the end of a triangular or rectangular (diving board) micromachined silicon cantilever. Used as surface probes in SPM. Typically, the radius of the tip is on the order of 10 nm. Spring constants of cantilevered tips range from 0.01 to 10 N/m.

Contact stiffness (S) The first derivative of a surface-restoring force with respect to out-of-plane surface displacement.

Continuum elastic theory Fundamental theory of the deformation of solids. Assumes that a system can be approximated as a completely continuous body, and that deformations due to external stresses are elastic (completely reversible).

Crystal defects Departures from a perfect, periodic structure in a crystal lattice. Typical defects include dislocations (extra or missing rows or planes of atoms), vacancies (missing atoms), interstitials (additional atoms between lattice sites), or disclinations (coordination number defects). Density functional theory (DFT) An analytic or numerical modeling technique (often for an electronic structure) wherein a local electronic or probability function is varia-tionally optimized to calculate the ground or excited states of a system.

Derjaguin, Muller, and Toporov theory (DMT theory) Theory of nanoscale deformation of a tip at an adhesive surface wherein surface adhesive forces are restricted to a fraction of the contact area.

Elasticity The quality of elastic response: linear dependence of restoring force on displacement. Finite-element analysis (FEA) A numerical modeling technique for which a continuous system (solid or fluid) is represented by a 3-D mesh or matrix of finite-sized elements. The response of the entire system to external stresses, temperature changes, applied fields, and so on is determined by solving classical equations of motion (Newton's equation, Maxwell's equations, Navier-Stokes equation, etc.) at the interfaces of each element. Force modulation microscopy (FMM) An implementation of SPM wherein the oscillation amplitude of a cantilevered tip in contact with a substrate is measured as the tip is scanned over a surface. For surfaces exhibiting a contact stiffness below the cantilever spring constant, such scans can reveal the spatial variation of surface mechanical properties. Graphene Referring to a hexagonal atomic structure of carbon as in a single a-b plane of graphite. Hertzian contact Model of a surface-surface contact for which only contact forces (short-range electrostatic forces) are considered. Long-range and adhesive forces are ignored. Heterodyne force microscopy (HFM) An implementation of SPM wherein heterodyne coupling of sample and cantilever ultrasonic vibrations (via the nonlinear-force displacement relationship of a scanning probe tip at a surface) is used to probe the nanometer spatial variations of surface visoelastic properties.

Integrated circuits (ICs) Semiconducting devices and associated electrical interconnects integrated on a single substrate via multilayer, photolithography-based processing. Johnson-Kendall-Roberts-Sperling theory (JKRS theory)

Theory of nanoscale deformation of a tip at an adhesive surface assuming the validity of classical elastic theory. Local density of states (LODS) In the context of the electronic properties of a material, the LDOS is the number of quantum mechanical states per unit volume that can be occupied by an electron.

Molecular dynamics (MD) Numerical modeling paradigm wherein an empirical or analytically derived potential is used to calculate atomic or molecular configurations based on the numerical solutions to the Newtonian or quantum mechanical equations of motion.

Mechanical resonance Dynamic condition wherein a mechanical system is driven at a natural vibration frequency. Microelectrical mechanical systems (MEMS) Term typically applied to 2-D or 3-D microstructures fabricated using the techniques of integrated-circuit fabrication. Nanocomposite A multicomponent composite material where the spatial size or modulation of at least one of the components is characterized by a nanometer-length scale. Nanoindentation Mechanical characterization technique wherein material modulus, hardness, and fracture strength are measured by indentation with a pyramidal or tetrahedral tip. The indentation is typically on the order of microns. Nanomaterials Engineered materials exhibiting unique properties resulting from the manipulation of the material structure or composition at the nanometer-length scale. Nanomechanical imaging Direct imaging of mechanical properties (modulus, visoelasticity, etc.) with nanometer-scale resolution via near-field microscopy. Nanomechanics The mechanics of nanometer-scale contacts and the deformation of nanoscale structures. Nanorope Term typically applied to bundles of nanotubes in a hexagonal arrangement forming a rope-like braid. Nanotribology The study of tribology (frictional interactions of surfaces) at the nanometer-length scale. Nanotube A nanometer-scale tube formed by wrapping single or multiple atomic layers in a cylindrical geometry. The former is referred to as a single-wall nanotube (SWNT). The latter is referred to as a multiwall nanotube (MWNT). Diameters range typically from 2 to >100 nm. Typically formed by graphene sheets of carbon nanotubes. Can also be formed by a number of other inorganic compounds. Organosilicates A term typically applied to solids or chemical compounds involving siloxane groups with organic lig-ands.

Piezoelectric The property of a material lacking inversion symmetry whereby application of physical stress results in a change in the polarization of the material. Conversely, application of an external voltage to a piezoelectric material will induce a spatial deformation.

Plasticity Nonelastic response of a material to an applied stress wherein a nonrecoverable (plastic) deformation is induced.

Poisson's ratio (a) Ratio of the transverse compression to the longitudinal extension of an object subjected to a tensile stress.

Quantum dot (QD) Term typically referring to nanometer-scale semiconductor particle (synthesized chemically in nanopowder form or grown on an appropriate substrate) exploited for unique electrical or optoelectronic properties due to quantum-mechanical localization phenomena. Reduced Young's modulus (Er = E/{1 — a2)) Conventional Young's modulus normalized by Poisson's ratio.

Shear modulus Typically defined as the ratio of the applied shear stress to the fractional transverse displacement of an object.

Scanning local acceleration microscopy (SLAM) An implementation of SPM whereby the deflection of the can-tilevered tip is proportional to the tip acceleration, and can be related to the mechanical properties of the substrate. Scanning probe microscopy (SPM) Any number of techniques in which a local probe is rastered across a surface with subnanometer precision to characterize topographic or material properties. Examples include scanning tunneling microscopy (STM), in which local tunneling currents between a scanning tip and a substrate are used to map the local density of electronic states, or atomic force microscopy (AFM), where the local deflection of a cantilevered tip by contact or van der Waals forces is recorded as the tip is scanned over a surface to measure surface topography. Tensile strength Typically defined as the longitudinal force or stress applied to a material for which nonreversible deformation results.

Tight-binding approximation (TB) An approximation for solving quantum-mechanical equations of motion for a material in which it is assumed that electrons are localized near the parent ion.

Ultrasonic force microscopy (UFM) An implementation of SPM wherein an out-of-plane ultrasonic vibration is applied to a sample on which a cantilevered tip (in contact) is scanned. For sufficient vibration amplitude, a tip-deflection signal proportional to the local sample modulus is obtained. van der Waals forces Weak, long-range forces resulting from induced electric dipole fields. Typically varies inversely as the separation to the sixth power.

Viscoelasticity Dynamics of elastic deformation, including the temporal response of materials to an elastic deformation.

Xerogel Trade name referring to a nanoporous silicate material.

Young's modulus (E) Typically defined as the ratio of the applied longitudinal stress to the fractional I longitudinal deformation of an object.

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