A theoretical description of incoherent spin dependent multiple scattering
of electrons at a single-crystal surface partially covered with a
disordered overlayer is reported. A formalism in which occupation operators
specify the occupancy of a chemisorption site is used for the statistical
description of a disordered adlayer. The theory is based upon the concepts
used in multiple-scattering DLEED theory. In the present considerations
spin effects are introduced to this theory by using the time independent
Dirac equation. Thus, a simple expression for incoherent spin dependent
intensity is obtained. The spin-orbit induced `up/down' asymmetry is then
calculated. As an example the particular case of CO/Pt(111) is examined. It
is found that diffuse SPLEED is sensitive to the geometrical parameters
characterizing the substrate/disordered adsorbate system as well as to the
parameters related to the statistical distribution of the occupied
chemisorption sites. It is demonstrated that the method is applicable to
any disordered surface suitable for DLEED investigation and in this way
enlarges the number of experimental data convenient for disordered surface
structure analysis.