snompy.fdm.geom_func_taylor

fdm.geom_func_taylor(z_tip, j_taylor, r_tip, L_tip, g_factor, d_Q0, d_Q1)

The height-dependent part of the separable Taylor series expression for the FDM.

Parameters:

z_tipfloat

Height of the tip above the sample.

j_taylorinteger

The corresponding power of the reflection coefficient in the Taylor series.

r_tipfloat

Radius of curvature of the AFM tip.

L_tipfloat

Semi-major axis length of the effective spheroid from the finite dipole model.

g_factorcomplex

A dimensionless approximation relating the magnitude of charge induced in the AFM tip to the magnitude of the nearby charge which induced it. A small imaginary component can be used to account for phase shifts caused by the capacitive interaction of the tip and sample.

d_Q0float

Depth of an induced charge 0 within the tip. Specified in units of the tip radius.

d_Q1float

Depth of an induced charge 1 within the tip. Specified in units of the tip radius.

Returns:

f_tcomplex

The height-dependent part of the separable taylor series expression for the bulk FDM.

See also

taylor_coef

Function that uses this to calculate the Taylor series coefficients for the bulk FDM.

Notes

This function implements the equation

\[f_{t} = f_0 f_1^{j-1}\]

where \(f_{t}\) is f_t, \(j\) is j_taylor, and \(f_j\) is a function encapsulating the geometric properties of the tip-sample system, implemented here as geom_func().