Pra.Ma.

31. 2.4.1 Qualitative consideration
(2. Scanning Force Microscopy (SFM)/2.4 Non-linear Oscillations of Cantilever)

Consider a cantilever oscillations when in addition to driving force ((1) in chapter 2.2.3.3), an external force acts on it. The equation of motion in this case is written as

32. 2.4.2 Analysis of cantilever motion (perturbation theory)
(2. Scanning Force Microscopy (SFM)/2.4 Non-linear Oscillations of Cantilever)

Consider one of the solution methods to the probe's tip equation of motion in an arbitrary potential (see formula (1) in chapter 2.4.1). Assume the tip of length is attache

33. 2.4.3 Method of resonance characteristics calculation. Approach-retraction curves
(2. Scanning Force Microscopy (SFM)/2.4 Non-linear Oscillations of Cantilever)

In chapter 2.4.2 we presented the approximate method of solution to the tip equation of motion in an arbitrary potential field. It was shown that the resonance charac

34. 2.4.4 Modeling of nonlinear oscillations
(2. Scanning Force Microscopy (SFM)/2.4 Non-linear Oscillations of Cantilever)

Let us study an oscillating cantilever behavior near a sample surface. Presented below is an interactive Flash model that allows to investigate changes in the character of re

35. 2.5.1 The effect of elastic deformations
(2. Scanning Force Microscopy (SFM)/2.5 Ultimate Resolution in Contact Mode)

The AFM technique accuracy is limited by elastic deformations which modify a sample topography. One of the effects of this kind, the indentation of large organic mole

36. 2.5.2 Effect of the tip curvature radius and cone angle
(2. Scanning Force Microscopy (SFM)/2.5 Ultimate Resolution in Contact Mode)

Despite the ability to reach high spatial resolution, the acquired surface topography image can sometimes not correspond to the real surface features due to the effec

37. 2.6.1 The nature of frictional forces
(2. Scanning Force Microscopy (SFM)/2.6 Probe-Sample Interaction: Lateral Forces)

Lateral forces (besides normal to the surface forces) arise from the tip-surface interaction. AFM allows to measure these forces thereby expanding surface analysis ab

38. 2.6.2 Cantilever deformations under the influence of lateral forces
(2. Scanning Force Microscopy (SFM)/2.6 Probe-Sample Interaction: Lateral Forces)

To investigate friction, the Lateral Force Microscopy (LFM) is used. It is based on the probe lateral deflection recording during scanning. In the LFM, the cantilevers in

39. 2.6.3 Calibration of the optical detection system
(2. Scanning Force Microscopy (SFM)/2.6 Probe-Sample Interaction: Lateral Forces)

Having got a notion about the relation between the lateral forces and cantilever deformations (see derivation), let us discuss the calibration of the detection unit. Tilts a and

40. 2.6.4 Qualitative interpretation of results
(2. Scanning Force Microscopy (SFM)/2.6 Probe-Sample Interaction: Lateral Forces)

The relation between detected signal and the lateral force acting in the x-direction is given by: , (1)

41. 2.6.5 Stick-slip motion on the nanoscale
(2. Scanning Force Microscopy (SFM)/2.6 Probe-Sample Interaction: Lateral Forces)

Introduction. The nanotribology aim is explanation and modeling of friction on the atomic scale. In contrast to microtribology which operates with notions

42. 2.6.6 Stick-slip phenomenon on the microscale
(2. Scanning Force Microscopy (SFM)/2.6 Probe-Sample Interaction: Lateral Forces)

ntroduction. In microtribology, the friction is considered on the continuum scale and against nanotribology, the atomic structure of matter is not taken in

43. 2.6.7 Appendices
(2. Scanning Force Microscopy (SFM)/2.6 Probe-Sample Interaction: Lateral Forces)

APPENDIX I. In the early model of the microscope Solver P47 the cantilever axis is inclined 20° to the sample plane (Fig. 1). The plane of incident and reflect

44. 2.7.1 MFM general concept
(2. Scanning Force Microscopy (SFM)/2.7 Magnetic Force Microscopy: Quantitative Result)

The magnetic force microscopy general concept is the registration of the force interaction between a magnetic probe and a sample's magnetic field. Today, there ar

45. 2.7.2 Algorithms for the physical parameters of the sample obtaining
(2. Scanning Force Microscopy (SFM)/2.7 Magnetic Force Microscopy: Quantitative Result)

What information about the sample magnetic properties can we reveal knowing the derivative of the magnetic interaction force with respect to vertical direction ?

46. 2.7.3 Interaction of the hard magnetic cantilever with the magnetic field of the studied sample (gen
(2. Scanning Force Microscopy (SFM)/2.7 Magnetic Force Microscopy: Quantitative Result)

If we know the magnetic field from the sample, then force acting on magnetic cantilever and its derivative in direction can be calculated by integrating the force acting on u

47. 2.7.4 Dipole effective magnetic moment approximation
(2. Scanning Force Microscopy (SFM)/2.7 Magnetic Force Microscopy: Quantitative Result)

Within the framework of the point dipole model the probe magnetic properties are considered to be entirely defined by its dipole effective magnetic moment as well as

48. 2.7.5 Effective monopole magnetic charge approximation
(2. Scanning Force Microscopy (SFM)/2.7 Magnetic Force Microscopy: Quantitative Result)

Along with the model of point dipole (see chapter 2.7.4), an alternative model of point monopole charge exists which allows to describe in some cases the cantilever inter

49. 2.7.6 Interaction between soft magnetic probe and magnet sample
(2. Scanning Force Microscopy (SFM)/2.7 Magnetic Force Microscopy: Quantitative Result)

In chapter 2.7.3 we described the general model of a hard magnetic probe interaction with a magnetic field of a sample and neglected the fact that a tip and a sample

50. 2.7.7 Interaction between paramagnetic probe and magnet sample
(2. Scanning Force Microscopy (SFM)/2.7 Magnetic Force Microscopy: Quantitative Result)

If magnetic field produced by a sample is known, then force on a magnetic cantilever and its derivative in direction can be calculated integrating the force acting on the ele

51. 2.7.8 Methods of magnet probe parameters estimation
(2. Scanning Force Microscopy (SFM)/2.7 Magnetic Force Microscopy: Quantitative Result)

At the present time there are a lot of MFM probes of various types [1]. The proper choice of a probe for studying a specific microstructure is sometimes an independent an

52. 2.7.9 Magnetic field of rectangular conductor with current
(2. Scanning Force Microscopy (SFM)/2.7 Magnetic Force Microscopy: Quantitative Result)

Let us calculate the spatial distribution of magnetic field generated by density current passing through a rectangular conductor having length , width and thickness , and (Fi

53. Appendices
(2. Scanning Force Microscopy (SFM)/2.7 Magnetic Force Microscopy: Quantitative Result)

Appendix 1. Calculation of the force and force gradient on a cylindrical ferromagnetic probe in the magnetic field of a conductor. Let us determine the force

54. IBM Scanning Tunneling Microscopy
(Web Links / SPM)

55. LEGO-AFM
(Web Links / Curiosità)

Un AFM dimostrativo fatto di LEGO.