snompy.fdm.refl_coef_qs_from_eff_pol_n

fdm.refl_coef_qs_from_eff_pol_n(alpha_eff_n, A_tip, n, z_tip=None, r_tip=None, L_tip=None, g_factor=None, d_Q0=None, d_Q1=None, n_trapz=None, n_tayl=None, beta_threshold=None, reject_negative_eps_imag=False, reject_subvacuum_eps_abs=False, eps_env=None)

Return the quasistatic reflection coefficient corresponding to a particular effective polarizability, demodulated at higher harmonics, using a Taylor series representation of the FDM.

Parameters:

alpha_eff_ncomplex

Effective polarizability of the tip and sample, demodulated at n.

A_tipfloat

The tapping amplitude of the AFM tip.

nint

The harmonic of the AFM tip tapping frequency at which to demodulate.

z_tipfloat

Height of the tip above the sample.

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.

n_trapzint

The number of intervals used by snompy.demodulate.demod() for the trapezium-method integration.

n_taylint

Maximum power index for the Taylor series in beta.

beta_thresholdfloat

The maximum amplitude of returned beta values determined to be valid.

reject_negative_eps_imagbool

True if values of beta corresponding to bulk samples with negative imaginary permitivitty should be rejected as invalid results.

reject_subvacuum_eps_absbool

True if values of beta corresponding to bulk samples with permitivitty whose magnitude is less than the vacuum permitivitty (1.0) should be rejected as invalid results.

eps_envarray_like

Permitivitty of the environment. Used to calculate the sample permitivitty when reject_negative_eps_imag or reject_subvacuum_eps_abs are True.

Returns:

betacomplex, masked array

Quasistatic reflection coefficient of the interface.

See also

taylor_coef

Function that calculates the Taylor series coefficients for the bulk FDM.

eff_pol_n_taylor

The inverse of this function.

Notes

This function is valid only alpha_eff_n values corresponding to`beta` magnitudes less than around 1.

This function solves, for \(\beta\): \(\alpha_{eff, n} = \delta(n) + \sum_{j=1}^{J} a_{j, n} \beta^j\), where \(\delta\) is the Dirac delta function \(\beta\) is beta, \(j\) is the index of the Taylor series, \(J\) is n_tayl and \(a_{j,n}\) is the Taylor coefficient, implemented here as taylor_coef().

There may be multiple possible solutions (or none) for different inputs, so this function returns a masked array with first dimension whose length is the maximum number of solutions returned for all input values. Values which are invalid are masked.