Karim R. Gadelrab

A method to provide rapid in situ determination of tip radius in dynamic atomic force microscopy

We provide a method to characterize the tip radius of an atomic force microscopy in situ by monitoring the dynamics of the cantilever in ambient conditions. The key concept is that the value of free amplitude for which transitions from the attractive to repulsive force regimes are observed, strongly depends on the curvature of the tip. In practice, the smaller the value of free amplitude required to observe a transition, the sharper the tip. This general behavior is remarkably independent of the properties of the sample and cantilever characteristics and shows the strong dependence of the transitions on the tip radius. The main advantage of this method is rapid in situ characterization. Rapid in situ characterization enables one to continuously monitor the tip size during experiments. Further, we show how to reproducibly shape the tip from a given initial size to any chosen larger size. This approach combined with the in situ tip size monitoring enables quantitative comparison of materials measurements between samples. These methods are set to allow quantitative data acquisition and make direct data comparison readily available in the community.

Mechanical properties of BixSb2−xTe3 nanostructured thermoelectric material

Research on thermoelectric (TE) materials has been focused on their transport properties in order to maximize their overall performance. Mechanical properties, which are crucial for system reliability, are often overlooked. The recent development of a new class of high-performance, low-dimension thermoelectric materials calls for a better understanding of their mechanical behavior to achieve the desired system reliability. In the present study we investigate the mechanical behavior of nanostructure bulk TE material p-type Bi(x)Sb(2-x)Te(3) by means of nanoindentation and 3D finite element analysis. The Youngs modulus of the material was estimated by the Oliver-Pharr (OP) method and by means of numerically assisted nanoindentation analysis yielding comparable values about 40 GPa. Enhanced hardness and yield strength can be predicted for this nanostructured material. Microstructure is studied and correlation with mechanical properties is discussed.

Energy dissipation distributions and dissipative atomic processes in amplitude modulation atomic force microscopy

Instantaneous and average energy dissipation distributions in the nanoscale due to short and long range interactions are described. We employ both a purely continuous and a semi-discrete approach to analyze the consequences of this distribution in terms of rate of heat generation, thermal flux, adhesion hysteresis, viscoelasticity and atomic dissipative processes. The effects of peak values are also discussed in terms of the validity of the use of average values of power and energy dissipation. Analytic expressions for the instantaneous power are also derived. We further provide a general expression to calculate the effective area of interaction for fundamental dissipative processes and relate it to the energy distribution profile in the interaction area. Finally, a semi-discrete approach to model and interpret atomic dissipative processes is proposed and shown to lead to realistic values for the atomic bond dissipation and viscoelastic atomic processes.

Disentangling viscosity and hysteretic dissipative components in dynamic nanoscale interactions

The mechanisms through which energy is dissipated in nanoscale dynamic interactions might involve tens or hundreds of atoms and might be diverse. Here, a method is presented that provides the means to disentangle, with the use of common experimental parameters, short and long range viscosity and hysteretic dissipative components. While the approach is general, the experimental study is directed to show the mechanisms of energy dissipation between a silicon atomic force microscope tip and a carbon nanotube and a quartz surface. By stabilizing the tip in situ, quantitative information is found in a reproducible manner where the magnitude of energy dissipated remains constant in experiments thus allowing comparative studies.

Heterogeneous Dissipation and Size Dependencies of Dissipative Processes in Nanoscale Interactions

Here, processes through which the energy stored in an atomic force microscope cantilever dissipates in the tip-sample interaction are first decoupled qualitatively. A formalism is then presented and shown to allow quantification of fundamental aspects of nanoscale dissipation such as deformation, viscosity, and surface energy hysteresis. Accurate quantification of energy dissipation requires precise calibration of the conversion of the oscillation amplitude from volts to nanometers. In this respect, an experimental methodology is presented that allows such calibration with errors of 3% or less. It is shown how simultaneous decoupling and quantification of dissipative processes and in situ tip radius quantification provide the required information to analyze dependencies of dissipative mechanisms on the relative size of the interacting bodies, that is, tip and surface. When there is chemical affinity, atom-atom dissipative interactions approach the energies of chemical bonds. Such atom-atom interactions are found to be independent of cantilever properties and tip geometry thus implying that they are intensive properties of the system; these interactions prevail in the form of surface energy hysteresis. Viscoelastic dissipation on the other hand is shown to depend on the size of the probe and operational parameters.

Investigation of nanoscale interactions by means of subharmonic excitation

Multifrequency atomic force microscopy holds promise as a method to provide qualitative and quantitative information about samples with high spatial resolution. Here, we provide experimental evidence of the excitation of subharmonics in ambient conditions in the regions where capillary interactions are predicted to be the mechanism of excitation. We also experimentally decouple a second mechanism for subharmonic excitation that is highly independent of environmental conditions such as relative humidity. This implies that material properties could be mapped. Subharmonic excitation could lead to experimental determination of surface water affinity in the nanoscale whenever water interactions are the mechanism of excitation.

The additive effect of harmonics on conservative and dissipative interactions

Multifrequency atomic force microscopy holds promise as a tool for chemical and topological imaging with nanoscale resolution. Here, we solve the equation of motion exactly for the fundamental mode in terms of the cantilever mean deflection, the fundamental frequency of oscillation, and the higher harmonic amplitudes and phases. The fundamental frequency provides information about the mean force, dissipation, and variations in the magnitude of the attractive and the repulsive force components during an oscillation cycle. The contributions of the higher harmonics to the position, velocity, and acceleration can be added gradually where the details of the true instantaneous force are recovered only when tens of harmonics are included. A formalism is developed here to decouple and quantify the viscous term of the force in the short and long range. It is also shown that the viscosity independent paths on tip approach and tip retraction can also be decoupled by simply acquiring a FFT at two different cantilever separations. The two paths correspond to tip distances at which metastability is present as, for example, in the presence of capillary interactions and where there is surface energy hysteresis.

Energy dissipation in the presence of sub-harmonic excitation in dynamic atomic force microscopy

Amplitude modulation atomic force microscopy allows quantifying energy dissipation in the nanoscale with great accuracy with the use of analytical expressions that account for the fundamental frequency and higher harmonics. Here, we focus on the effects of sub-harmonic excitation on energy dissipation and its quantification. While there might be several mechanisms inducing sub-harmonics, a general analytical expression to quantify energy dissipation whenever sub-harmonics are excited is provided. The expression is a generalization of previous findings. We validate the expression via numerical integration by considering capillary forces and provide experimental evidence of sub-harmonic excitation for a range of operational parameters.

Quantification of dissipation and deformation in ambient atomic force microscopy

A formalism to extract and quantify unknown quantities such as sample deformation, the viscosity of the sample and surface energy hysteresis in amplitude modulation atomic force microscopy is presented. Recovering the unknowns only requires the cantilever to be accurately calibrated and the dissipative processes occurring during sample deformation to be well modeled. The theory is validated by comparison with numerical simulations and shown to be able to provide, in principle, values of sample deformation with picometer resolution.

Single-cycle atomic force microscope force reconstruction: resolving time-dependent interactions

Here, we enhance the capabilities of the atomic force microscope (AFM) to show that force profiles can be reconstructed without restriction by monitoring the wave profile of the cantilever during a single oscillation cycle. Two approaches are provided to reconstruct the force profile in both the steady and transient states in what we call single-cycle measurements. The robustness of the formalism is tested numerically to recover complex but relevant interactions. With single-cycle measurements, we add high temporal resolution (possibly microsecond range) to the spatial resolution of AFM. The access to simultaneous high throughput and high sensitivity further opens the door to a variety of feedback options for imaging.