research papers
If the unit-cell distribution of atomic mean-square displacement parameters B = 8π2〈u2〉 is assumed to be normal, with mean µ = 〈B〉 and variance σ2 = , the statistical expectation value of the Debye-Waller factor W2 = exp(−2Bs2), where s = (sin θ)/λ, is 〈W2〉 = exp[−2(µ − σ2s2)s2]. This result has been incorporated into procedures for scaling and normalizing measured Bragg intensities to their Wilson expectation values. The procedures can determine both isotropic µ(B) and σ(B) and anisotropic µ(Uij) and σ(Uij distribution parameters. Tests with experimental data and refined structural models for several protein crystals show that the procedures yield reliable normalized structure-factor amplitudes for direct-methods applications, with values of R = averaging 5%.