calculate X-ray absorption coefficient

[toqduj]

There are some hints in the documentation on how to calculate the X-ray absorption coefficient (from f2?? or by using the imaginary component of the sld?) using periodic table, but I can't figure it out... how would this be calculated (in 1/m for example) from the formula, density and wavelength, and can there be a convenience method for this?

I tried applying the relations in the table from http://gisaxs.com/index.php/Absorption_length to the imaginary part output by pt.xray_sld(material, energy=energy_keV, density=self.density), but that doesn't seem to be right.

[pkienzle]

For sld I'm using:

sld = ρ/m N_A re (f1 + f2 j)

with mass density ρ, molar mass m, Avogadro number N_A, and electron radius re.

So it should be:

μ = 2 λ Im{sld}

Because sld is in units of 1e-6/Ų and λ from xray_wavelength(keV) is in Å, need to scale by 1e4 to get 1/m.

I can reproduce the figures in the link using:

# Reproduce plots in http://gisaxs.com/index.php/Absorption_length
def do():
    import numpy as np
    import matplotlib.pyplot as plt
    import periodictable as pt
    from periodictable.constants import avogadro_number as Na
    from periodictable.xsf import xray_wavelength
    def None_to_nan(v):
        if v is None:
            return np.nan
        elif np.isscalar(v):
            return v
        else:
            return [np.nan if vk is None else vk for vk in v]
    fig, ax = plt.subplots(1, 2)
    for E in (2, 4, 8, 12, 16, 24): # energy in keV
        λ = xray_wavelength(E) # keV => Å
        z = np.array([el.number for el in pt.elements])
        ρ = np.array([None_to_nan(el.density) for el in pt.elements]) # g/cm³
        m = np.array([el.mass for el in pt.elements]) # g/mol
        sld = np.array([None_to_nan(el.xray.sld(energy=E)) for el in pt.elements]) # 1e-6/Ų
        μ = 2*λ*sld[:,1]*1e-6 # 1/Å
        #σ = 1e8 * μ*m / (Na*ρ) # Å/cm • 1/Å • g/mol / (1/mol • g/cm³) = cm² 
        ax[0].plot(z, 1e-4 * 1/μ, label=f"{E} keV") # 1e-4 μm/Å
        ax[1].plot(z, 1e4 * μ/ρ, label=f"{E} keV") # 1e8 Å/cm • 1e-4 m²/cm² • 1/Å / (g / cm³) = m²/g 
    ax[0].legend()
    ax[0].set_xlabel("atomic number, Z")
    ax[0].set_ylabel("Absorption length (μm)")
    ax[0].set_yscale("log")
    ax[0].set_ylim(1e-1, 1e5)

    ax[1].set_xlabel("atomic number, Z")
    ax[1].set_ylabel("μ/ρ (m²/g)")
        
do()

[pkienzle]

BTW, this is given in the right hand column of the "related forms" table further down in the page: http://gisaxs.com/index.php/Absorption_length#Related_forms