Forces
The Probe Particle (AFM) Model calculates all the forces that affect the Probe Particle:
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Forces caused by the interaction with (metallic) tip
- The lateral forces - x and y are holding the tip in its equilibrium position from its lateral sides. These forces are harmonic (spring) forces. For CO they are around 0.24 N/m. Note: For the Double Probe Particle model different forces are used, see its wiki.
- The radial force - R is holding the Probe Particle in the appropriate distance bellow the last metallic-tip atom. !!! Unlike in the original Fortran code and the paper this force is also harmonic (spring) !!! - This allows for better computational stability, than the original Lennard-Jones (L-J) model. L-J could in extreme cases lead to the loss of Probe Particle, which is physically right, but the exact constant is unknown and is extremely tip-dependent. Anyway, if the Probe Particle/tip-apex is lost in theory or experiment it causes loss of high resolution and the results are generally not usable. From our experience the usage of less precise potential is not causing any additional problems with the usage of spring constant around 20.0 or 30.0 N/m.
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Forces caused by the interaction with the sample
- Pauli repulsion and attractive London dispersion, which are approximated by the Lennard-Jones (L-J) model. The total force is pre-calculated and stored in
FFLJ_?.xsf or FFLJ_?.npyfiles. The force is calculated as a sum of forces originating from all the sample atoms. The parameters for elements are stored in atomtypes.ini file. You can copy and adjust this file in the local directory of calculations. The model will read it automatically. (In the more recent development OpenCl branches other models are available as well). - Electrostatics forces, which can be calculated multiple ways: a) From local charges or from Hartree potential calculated from DFT (or generally electronic-structure) calculations. Usage of multipoles is available for both of methods, too. The multipole moment is calculated by
Q*sigmafor dipole orQ*sigma*sigmafor quadrupole. These forces are also precalculated. Since the charge of the tip is experiment dependent and sometimes needs to be tested. The forces are rescaled anytime the relaxation is performed.
- Pauli repulsion and attractive London dispersion, which are approximated by the Lennard-Jones (L-J) model. The total force is pre-calculated and stored in
During the relaxation, all the forces are taking into account and once a new equilibrium is found the code calculates the forces acting on the metallic forces. These tip forces can be either plotted or used for computation of the frequency shift.