Index. C Calibration of normal force, 261 of photodiode, 271 of cantilever spring constant

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1 Index A Adhesion, 106 maps, 244 Approach curve, 240 Atomic force microscope (AFM) current trends, overview, 16 computer simulations, 293 general principles, 11 generic system, 195 Autocorrelation, 182 B B, bulk modulus, 33 Boiling temperature liquids, correlated to dipole moment, 40 liquids, correlated to molecular mass, 23 liquids, correlated to molecular shape, 23 Boltzmann factor, 55 Bond strength, typical, 140 Bulk modulus (B) defined, 133 compared to shear modulus, 138 C Calibration of normal force, 261 of photodiode, 271 of cantilever spring constant added mass, 269 hydrodynamic damping, known spring constant, 268 thermal noise, 262 Cantilever Bernoulli-Euler assumption, 174 calibration benchmarks, 270 deflection, 201 dynamic beam, 171 sinusoidal excitation by dither piezo, 211 by Lorentz Force, 212 by time varying magnetic field, 211 by photothermal effect, 212 static deflection, 164 torsion, 203 Chemical bond, 33 Chemical force microscopy, 147 Coarse approach, 232 Computer simulations, 293 Contact mechanics conical tip, 141 cylindrical punch, 141 Boussinesq, 141 sphere-flat plane DMT, 146 Hertz,

2 320 Fundamentals of Atomic Force Microscopy, Part I Foundations JKR, 149 M-D, 152 relevance to AFM, 131, 143 Contact mode advantages of, 250 AFM, 229 applications of, 250 compared to non-contact mode, 16, 252 disadvantages of, 250 error map, 250 feedback control, 284 forward, backward scans, 250 general definition, 13 imaging, 247 repulsive regime, 249 simulation of, 306 Contact pressure of AFM tip, 146, 251 Contact area, 145, 253 Control electronics, 216 Coulomb s law, 25 Cantilever area moment, 170 calibration of normal force, 261 added mass, 269 hydrodynamic damping, known spring, 268 thermal fluctuations, 262 curvature defined, 167 deflection at free end, 169 displacement along, 169, 176 displacement at end, 169 distributed load, 173 dynamic beam, 171 internal moments bending, 172 defined, 165 shear, 172 modal mass, 267 modes, 178 mode shapes, 180 rotation at free end, 170 slope, 170, 177 spring constant, 169, 178 static deflection, 164 rms deflection, 181 thermal fluctuations, 180, 262 torsion, 203 vibrating beam, 178 Cellulose nanocrystalline filament, 246 D Debye interaction, 67, 75 Density of atoms in chemical elements, 100 of a gas, 267 mass per unit length, 178 mass per unit volume, 178 Derajaguin approximation, 112 Dielectric function evaluation of Hamaker constant, 121 frequency dependence, 120, 123 imaginary part, 123 imaginary frequencies, 124 real part, 123 Dipole moment molecular, calculation of, 38 momentary, fluctuating, 77 definition, 39 potential energy in external E-field, 41 DLP theory, 119 DMT contact relevant parameters, 146 force vs. z-displacement, 241 simulation of, 301 Dupre equation, 147 Dynamic force microscope dynamic mode imaging, 15 E E, Young s modulus, 133 Elasticity map, 244 Electron microscope, 3, 4 Electrostatic potential energy definition, 28

3 Index 321 Electronegativity, 35 Effective noise bandwidth, 189 Entropy, 29 Equipartition theorem, 180, 263 Error signal, 196 Error map, 250, 288 F Feedback in AFMs, 197 integral gain, 215, 285 frequency response, 285 general principle, 213 loop, operation of, 284 optimal settings, 285 proportional gain, 215, 285 response to step discontinuity, 286 sampling frequency, 215 simulation of, 30 Zeigler-Nichols tuning rule, 287 Field-ion microscope, 3 Filtering noise, 189 Flexure translation stage, 210 Force spectroscopy, 235 Force vs. distance see Force vs. z-displacement Force vs. z-displacement, 13, 230 co-ordinate system, 231 DMT contact model, 241 d vs. z, 242 q vs. z, 242 four characteristic features, 232 loading and withdrawal, 239 on cellulose filaments, 247 substrate (sample) location, z, 230 time domain, 246 tip deflection, q, 230 tip-substrate distance, d, 230 typical data, 233 Frictional Force Microscope (FFM), 255 Friction coefficient of, 254 frictional force, 253 macroscale, 254 G G, shear modulus, 133 H Hamaker constant, defined, 99 constant, values in literature, 99 calculated from DLP theory, 121 estimated from DMT model, 244 interaction, 95 interaction, limitations of, 101 Heisenberg uncertainty principle, 118 Hertz interaction simulation of, 299 Hertz contact relevant parameters, 144 Hook s Law, 77, 175 Hydrodynamic damping of cantilever, I Image acquisition time, typical, 282 Image processing plane subtraction, 283 scan rotation, 282 Image size, typical, 249 Interaction between micron-size objects, 95 non-polar molecule and ion, 64 non-polar molecule and non-polar molecule, 77 non-polar molecule and polar molecule, 74 polar molecule and ion, 51 polar molecule and non-polar molecule, 74 polar molecule and polar molecule, 67 Interaction energy angle-average, thermal average, 59 Interface, 102

4 322 Fundamentals of Atomic Force Microscopy, Part I Foundations Intermittent-contact mode comparison, 16 general definition, 14 Intermolecular forces general discussion, 22 J JKR contact contact radius vs. applied force, 151 deformation vs. applied force, 151 relevant parameters, 149 Jump-to-contact during tip-substrate approach, 236 elimination of, 237 occurrence, 14 Jumping mode images general definition, 15 comparison, 16 K Keesom interaction, 67, 73 L Laser beam bounce, 198 Laser focal spot size, 198 spatial intensity, 198 Laser Doppler vibrometer, 264 Lateral signal, 204 Lateral force imaging, 253 Lennard-Jones, 36 Loading curve, 239 London interaction, 67, 77 M Maps of elasticity and adhesion, 244 Maugis-Dugdale comparison to DMT, JKR and Hertz, 155 definition of λ, 153 description of, 154 interpolation between DMT and JKR, 152 Matsubara frequencies, 120 Molar mass of various gasses, 268 N nanohub, 293 Non-contact mode advantages, 253 attractive regime, 251 compared to contact mode, 16, 252 constant height, 253 disadvantages, 252 general definition, 14 imaging, 250 Non-contact dynamic mode, 252 Non-polar molecule interacting with ion, 64 interacting with non-polar molecule, 77 interacting with polar molecule, 74 Normal signal, 204 O Optical deflection, 12, 200 Optical gain, estimation of, 202 Optical lever sensitivity, 274 P Particulate contamination, 276 Piezoelectric scanners bar scanners, 206 capacitance of, 209 creep, 208 electric polarization, 205 hysteresis, 208 non-linear behavior, 276 orthogonality between X and Y, 277 poling, 205 PZT ceramics, 205 tube scanners, 209

5 Index 323 Photodiode component of AFM, 196 calibration, 234 calibration process, 271 optical lever sensitivity (OLS), 274 use as position sensitive detector, 201, 203 segmented, 204 voltage, 232 Plane subtraction, 283 Poisson ratio defined, 135 table for chemical elements, 137 table for common materials, 138 Potential interaction energy, U for ion-dipole, 50 for molecule-molecule, 66 for van der Waals interaction, 82 Polar molecule interacting with ion, 51 interacting with non-polar molecule, 74 interacting with polar molecule, 67 Polarizability non-polar molecule, 62 Power spectral density (PSD), 184, 263 Q Quantum tunneling, 6 R Random fluctuations, 181 autocorrelation, 182 effective noise bandwidth, 189 Parseval s Theorem, 188 power spectral density, 184 Reynold s number, 267 Root mean square, 181 Rotated scan direction, 282 S Sader s hydrodynamic calibration, Scan speed simulation, 311 Scanning probe microscope (SPM) general principles, 2 comparison to TEM, SEM, 5 Scanning tunneling microscope (STM) general principles, 5 Scanning waveforms fast scan waveform, 280 slow scan waveform, 280 Schrödinger equation, 78 Set point, 197 Shear Modulus compared to bulk modulus, 138 defined, 133 Simulations, computer, 293 Standard calibrated substrates for X-Y calibration, 275 for Z-calibration, 279 Surface energy chart of chemical elements, 107 common materials, 106 contributions to, 106 defined, 103 estimated using Hamaker theory, 109 liquid-solid interface, 108 rough estimate of, 103 solid-solid interface, 108 table, 106 Surface topography, 249 T Tilt compensation, 283 Tip characterization, 247, 251 Tip dilation, simulation of, 309 Tip-sample interaction, 155 Tip shape measurement of, 246 simulation of, 309 Tip speed, 282

6 324 Fundamentals of Atomic Force Microscopy, Part I Foundations Tip-substrate force transducing, 198 Tip wear, 250, 253 Thermal averaging ion-dipole, angle averaged, 56 dipole-dipole, angle averaged, 71 Thermal drift, 217 Thermal expansion coefficients, typical, 218 Thermal noise, 262 Thermal tuning, 264 U U, interaction potential energy defined, 31 for ion-dipole, 50 for molecule-molecule, 66 for van der Waals interaction, 82 V van der Waals (vdw) attractive between non-polar molecules, 81 equation of state, gasses, 22 interaction, 82 momentary dipole fluctuation, 78 quantum dipole model, 77 surface interaction, 13 VEDA computer simulations contact mode simulation, 306 default parameters, 298 documentation, 298 feedback simulation, 311 flowchart, 297 force distance tool, 304 force viewer tool, 299 homepage of VEDA, 296 introduction, 293 list of simulation tools, 293 output options, 298 scan speed simulation, 311 timed-out simulation, 307 tip dilation, 309 tip-substrate interaction simulation, 298 utility of, 293 worksheet for input parameters, 313, 314 Vibrations, source of noise attenuation of, 222 floor, 219 NIST-A1 criteria, 221 octave band frequencies, 220 vibration criteria (VC), 221 VC-E criterion, 221 X X-Y scanner non-linear, 276 orthogonality, 275 Y Young s modulus (E) chart of chemical elements, 134 defined, 133 ranges for different materials, 135 related to bulk modulus, 139 related to shear modulus, 139 table of values, 136 Z Ziegler-Nichols tuning rule, 287 Z-positioner AFM component, 196 calibration constant, 231 calibration using miscut single crystal, 277 calibration using periodic trenches, 278 non-linearity, 279