W0334

Error Analysis for PDF Modeling. Simon J. L. Billinge^a and Brian H. Toby^b, ^aDept. of Physics and Astronomy, Michigan State Univ., East Lansing, MI 48824 and ^bNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg MD 20899.

This presentation demonstrates how statistical errors (standard uncertainties, s.u.) may be established for parameters determined from PDF analysis in a manner identical to that used for crystallographic analysis. The s.u. values from PDF analysis may well be lower than those from Rietveld analysis, since observations over a much wider Q-range are used in the former method.

When least-squares methods are used to fit a model to a PDF, the correlation between G(r) values must be treated by constructing a weight matrix, W_jk=__iⁿQ_i²_Q_i²sin(Q_ir_j)sin(Q_ir_k)_^__S(Q_i)]. The least-squares Hessian is then H= A^TWA, where A is the design matrix, A_ij = _M_i/_p_j, and where p are the parameters and M(p,x_i) is the model. The diagonal terms in the variance-covariance matrix, H^-1, can be used to determine statistical uncertainties, as is done for crystallographic refinements.