text: Le Bail analysis fits parameters using a steepest descent minimization process. Specifically, the method is least squares analysis, which is an iterative process that is discussed later in this article. The parameters being fitted include the unit-cell parameters, the instrumental zero error, peak width parameters, and peak shape parameters. First, the Le Bail method defines an arbitrary starting value for the intensities (I). This value is ordinarily set to one, but other values may be used. While peak positions are constrained by the unit cell parameters, intensities are unconstrained. The equation to calculate intensities is:
  In the equation, I is the intensity observed at a particular step and y(obs) is the observed profile point. y(calc) is the  A single intensity value may contain more than one peak. Other peaks may be calculated similarly. The final intensity for a peak is calculated as y(calc) = y(1) + y(2). The summation is carried out over all contributing profile points for a particular 2-theta bin. The summation process is known as profile intensity partitioning, and it works over any number of peaks. Le Bail technique works especially well with overlapping intensities since in this method the intensity is allotted based on the multiplicity of the intensities that contribute to a particular peak.
  The somewhat arbitrary choice of starting values produces a bias in the calculated values. The refinement process continues by setting the new calculated structure factor to the observed structure factor value. The process is then repeated with the new structure factor estimate. At this point, the unit cell, background, peak widths, peak shape, and resolution function are refined, and the parameters are improved.  The structure factor is then reset to the new structure factor value, and the process begins again. Structural refinement can continue with whole profile fitting techniques or further treatment of peak overlap. Probabilistic approaches may also be used to treat peak overlap.