f k ( q → → ) is the atomic form factor of the atom k ; it determines how the distribution of scattering matter about the nuclear position influences scattering. T k ( q → → ) is the atomic Debye–Waller factor; it determines how the propensity for nuclear displacement from the reference lattice position influences scattering. The expression given for DWF in the article's opening is different because of 1) the decision to take the thermal or time average, 2) the arbitrary choice of negative sign in the exponential, and 3) the decision to square the factor (which more directly connects it to the observed intensity).