feat: add functions to calculate δ, β, n, and k components of the ind…

periodictable/xsf.py

@@ -465,6 +465,155 @@ def index_of_refraction(compound, *, density=None, natural_density=None,
                       wavelength=wavelength)
     return 1 - wavelength**2/(2*pi)*(f1 + f2*1j)*1e-6
 
+def delta(compound, *, density=None, natural_density=None,
+                        energy=None, wavelength=None):
+    """
+    Calculates the δ component of the index of refraction for a given compound
+
+    :Parameters:
+        *compound* : Formula initializer
+            Chemical formula.
+        *density* : float | |g/cm^3|
+            Mass density of the compound, or None for default.
+        *natural_density* : float | |g/cm^3|
+            Mass density of the compound at naturally occurring isotope abundance.
+        *wavelength* : float or vector | |Ang|
+            Wavelength of the X-ray.
+        *energy* : float or vector | keV
+            Energy of the X-ray, if *wavelength* is not specified.
+
+    :Returns:
+        *delta* : float or vector | unitless
+            δ component of the index of refraction of the material at the given energy
+
+    :Notes:
+
+    Formula taken from http://xdb.lbl.gov (section 1.7) and checked
+    against http://henke.lbl.gov/optical_constants/getdb2.html. 
+    """
+    if energy is not None:
+        wavelength = xray_wavelength(energy)
+    assert wavelength is not None, "scattering calculation needs energy or wavelength"
+    f1, f2 = xray_sld(compound,
+                      density=density, natural_density=natural_density,
+                      wavelength=wavelength)
+    return wavelength**2/(2*pi)*(f1)*1e-6
+
+def beta(compound, *, density=None, natural_density=None,
+                        energy=None, wavelength=None):
+    """
+    Calculates the β component of the index of refraction for a given compound
+
+    :Parameters:
+        *compound* : Formula initializer
+            Chemical formula.
+        *density* : float | |g/cm^3|
+            Mass density of the compound, or None for default.
+        *natural_density* : float | |g/cm^3|
+            Mass density of the compound at naturally occurring isotope abundance.
+        *wavelength* : float or vector | |Ang|
+            Wavelength of the X-ray.
+        *energy* : float or vector | keV
+            Energy of the X-ray, if *wavelength* is not specified.
+
+    :Returns:
+        *beta* : float or vector | unitless
+            β component of the index of refraction of the material at the given energy
+
+    :Notes:
+
+    Formula taken from the equation
+
+    .. math::
+
+        n = 1 - \delta + i \beta
+
+    derivitive of the formula http://xdb.lbl.gov (section 1.7) using a more common
+    sign convention for the imaginary part of the index of refraction. Checked 
+    against http://henke.lbl.gov/optical_constants/getdb2.html. 
+    """
+    if energy is not None:
+        wavelength = xray_wavelength(energy)
+    assert wavelength is not None, "scattering calculation needs energy or wavelength"
+    f1, f2 = xray_sld(compound,
+                      density=density, natural_density=natural_density,
+                      wavelength=wavelength)
+    return wavelength**2/(2*pi)*(f2)*1e-6
+
+def n(compound, *, density=None, natural_density=None,
+                        energy=None, wavelength=None):
+    """
+    Calculates the real part (n) of the index of refraction for a given compound
+
+    :Parameters:
+        *compound* : Formula initializer
+            Chemical formula.
+        *density* : float | |g/cm^3|
+            Mass density of the compound, or None for default.
+        *natural_density* : float | |g/cm^3|
+            Mass density of the compound at naturally occurring isotope abundance.
+        *wavelength* : float or vector | |Ang|
+            Wavelength of the X-ray.
+        *energy* : float or vector | keV
+            Energy of the X-ray, if *wavelength* is not specified.
+
+    :Returns:
+        *n* : float or vector | unitless
+            n component of the index of refraction of the material at the given energy
+
+    :Notes:
+
+    Formula taken from the equation
+
+    .. math::
+
+        n = 1 - \delta
+
+    derivitive of the formula for δ from http://xdb.lbl.gov (section 1.7) using a more common
+    sign convention for the imaginary part of the index of refraction. Checked 
+    against http://henke.lbl.gov/optical_constants/getdb2.html. 
+    """
+    return 1 - delta(compound, 
+                      density=density, natural_density=natural_density, 
+                      energy=energy, wavelength=wavelength)
+
+def k(compound, *, density=None, natural_density=None,
+                        energy=None, wavelength=None):
+    """
+    Calculates the imaginary part (k) of the index of refraction for a given compound
+
+    :Parameters:
+        *compound* : Formula initializer
+            Chemical formula.
+        *density* : float | |g/cm^3|
+            Mass density of the compound, or None for default.
+        *natural_density* : float | |g/cm^3|
+            Mass density of the compound at naturally occurring isotope abundance.
+        *wavelength* : float or vector | |Ang|
+            Wavelength of the X-ray.
+        *energy* : float or vector | keV
+            Energy of the X-ray, if *wavelength* is not specified.
+
+    :Returns:
+        *k* : float or vector | unitless
+            k component of the index of refraction of the material at the given energy
+
+    :Notes:
+
+    Formula taken from the equation
+
+    .. math::
+
+        n = 1 - \delta + i \beta
+
+    derivitive of the formula for β from http://xdb.lbl.gov (section 1.7) using a more common
+    sign convention for the imaginary part of the index of refraction. Checked 
+    against http://henke.lbl.gov/optical_constants/getdb2.html. 
+    """
+    return beta(compound, 
+                density=density, natural_density=natural_density, 
+                energy=energy, wavelength=wavelength)
+
 def mirror_reflectivity(compound, *, density=None, natural_density=None,
                         energy=None, wavelength=None,
                         angle=None, roughness=0):