Scattering Length Density Calculator

Usage notes:

(3-28-2002) We are currently in the process of updating the way that the incoherent macroscopic cross section is calculated. The first number given is the incoherent cross section due to the spin of the nucleus (the one given in tables of the incoherent cross section). The second number given is the disordered scattering that would result if the atoms in your material were completely randomly distributed, for instance, if you had an alloy with no way of predicting which atom was going to be at a given site in the crystal. If your material is perfectly ordered all of the intensity due to the second term would go into coherent peaks. The actual incoherent scattering in your sample is somewhere between the two numbers depending on how ordered the sample is.

To calculate scattering length densities enter a compound and a mass density and click "Calculate". The first calculation will take the longest because the program has to download all of the data tables of neutron and x-ray scattering lengths, but it should be faster after that is performed.

It is not necessary to enter a number into the wavelength field. The wavelength is used to calculate the absorption cross section. The default wavelength is 1.8 Angstroms. If a value is entered into this field the absorption cross section will be scaled as wavelength/1.8 since the cross section data is given for 1.8 Angstrom (2200 m/s, 0.0253 eV, thermal) neutrons.

The 1/e length is the length of material that it will take to attenuate the beam to an intensity of 1/e (about 0.37) of its incident intensity. It is calculated as 1/(Sigma_inc + Sigma_abs) where Sigma_inc and Sigma_abs are, respectively, the macroscopic incoherent scattering and absorption cross sections calculated above.

Caveat on 1/e length: This number is a lower limit since only the incoherent and absorption cross sections are included in the calculations. Using the incoherent scattering gives a reasonable lower limit, but including the conherent scattering (which would be necessary to give a definite number for the attenuation) gives an unreasonable upper limit since the coherent scattering is highly structure dependent.

The first calculation will take a few seconds as the database of isotopes is downloaded to your browser, but any further calculations will be nearly instantaneous.

Specific isotopes are specified by putting the mass number in parenthesis after the symbol.

Element Symbols are case sensitive.

Only integer stoichiometry is supported at this time. If there is sufficient interest I will add non-integer stoichiometry. Until it is added you can use factors of 10 to do non-integer stoichiometry. For instance if you wanted to calculate Pd_1.3Si you can enter it as Pd13Si10, and as long as the density is correct it will calculate it correctly.

Examples of how to format the compound name:

• SiO2 (silicon dioxide)
• H20 (water)
• H(2)2O (heavy water), can also be written as D2O
• A 50% mixture of H2O and D2O can be calculated as follows: The mass densities of H20 and D2O are 1.0 and 1.1 g/cm^3, respectively. A 50-50 mixture of the two would then have a mass density of 1.05 g/cm^3. Write this mixture of H2O and D2O as H2OD2O or more simply as HDO. Other compositions can be calculated as well, for example a 70-30 mixture of H2O/D2O can be written as H14O7D6O3 or more simply H7D3O5 (i.e. 7 hydrogens, 3 deuteriums, and 5 oxygens) and the mass density calculated based on the percentages of H and D.
• C(13)6H(2)12O(18)6 (6 Carbon-13 atoms, 12 deuterium atoms, and 6 Oxygen-18 atoms)

To see what isotopes can be included in these calculations look at Neutron Scattering Lengths and Cross Sections on the web. All of the isotopes contained in that site are included in this calculator.

Report errors or make inquiries to Alan Munter, <alan.munter@nist.gov>