Absorption Coefficient Calculator

How strongly a compound absorbs X-rays, as the mass coefficient μ/ρ and the linear coefficient μ. It is μ that decides whether a measurement needs an absorption correction, and what crystal size to aim for.

You supply: A chemical formula — brackets and charges included — and a density, or tick the box and let it estimate the density from the formula.
Reading it: μ/ρ is a property of the substance alone; μ also depends on the density and is the one to judge. For Cu radiation it should not exceed 10 mm⁻¹.

Worked examples: NaCl · a nickel complex

Input

Results

chemical formula:	C₃₂H₂₆N₂O₂Ni₁
molar mass:	529.2556 g/mol
density:	1.237 g/cm³
mass absorption coefficient (Mo):	μ/ρ = 5.77 cm²/g
mass absorption coefficient (Cu):	μ/ρ = 9.52 cm²/g
linear absorption coefficient (Mo):	μ = 7.135 cm^-1 = 0.714 mm^-1
linear absorption coefficient (Cu):	μ = 11.78 cm^-1 = 1.178 mm^-1

How this is calculated

$μ = \frac{μ}{ρ} \times ρ$

$μ (Mo) = 5.76822 {cm}^{2} / g \times 1.237 g/ {cm}^{3} = 7.135 {cm}^{- 1}$

$\frac{I}{I_{0}} = \exp (- μ t)$ — the fraction of the beam that gets through a sample of thickness t.

For a crystal 0.1 mm across (t = 0.01 cm): $\frac{I}{I_{0}} = \exp (- 7.135 {cm}^{- 1} \times 0.01 cm) = 93.1 %$ transmitted.

The other radiations differ only in the mass absorption coefficient, which is a property of the elements present and of the wavelength. The 0.1 mm thickness is an illustration, not a property of your sample.

Notes and references

Generally, Mo radiation provides a higher resolution and more reflections compared to Cu radiation and should thus be considered to be the standard case. Cu radiation yields better reflection intensities, which is useful especially for weakly scattering crystals.
When the absolute configuration of a chiral compound is to be resolved (see also: Friedif Calculator) or a very large unit cell is expected, Cu radiation may be preferable.
The linear absorption coefficient of matter towards Cu radiation is generally higher and should not exceed 10 mm^-1.
for an exemplary calculation, see here
mass absorption coefficients taken from here (1 ≤ Z ≤ 83; based on H. P. Klug and L. E. Alexander, X-Ray Diffraction Procedures: For Polycrystalline and Amorphous Materials, Wiley, 2nd edn., 1974.)
atomic masses are abundance-weighted means derived from the NIST Atomic Weights and Isotopic Compositions dataset shipped with this site — the same data the Isotope Pattern Calculator uses, so a molar mass and the isotope pattern beside it cannot disagree (1 ≤ Z ≤ 108, up to hassium). The 26 elements with no stable isotopes have no measured atomic weight at all; they carry the mass number of their longest-lived isotope, which is a nominal figure, and the results say so when one is used.
for the estimation of crystal densities, the very rough assumption of an atomistic volume of 18 Å³ per non-hydrogen atom is made