The photoloc technique can permit the measurement of not only the state-to-state differential cross section but also its complete product polarization dependence for all moments of orientation and alignment with k less than or equal to 2. We have realized this possibility for the reaction Cl + C2D6 --> DCl(upsilon' = 0,J' = 1) + C2D5 at a collision energy of 0.25 eV, for which we have measured the differential cross section, 1/sigma(d sigma(00)/d Omega(r)), and the four polarization-dependent moments of the differential cross section, A(1)((1)stf), A(0)((2)stf), A(1)((2)stf), and A(2)((2)stf), in the stationary target frame (STF), which are defined by A(q)((k)stf) = (d sigma(kq)(stf)/d Omega(r))/(d sigma(00)/d Omega(r)). For the Cl + CD4 --> DCl(upsilon' = 0,J' = 1) + CD3 reaction at a collision energy of 0.28 eV we have also determined 1/sigma(d sigma(00)/d Omega(r)) and A(0)((2)stf). The laboratory speed distributions of the DCl(upsilon' = 0,J' = 1) products are measured using 2 + 1 resonance-enhanced multiphoton ionization (REMPI) and the core-extraction technique. The polarization-dependent differential cross sections are determined from the dependence of the core-extracted profiles on the photolysis and probe polarizations. Recent studies have shown that the Cl + CD, and Cl + C2D6 both show scattering behavior described by the line-of-centers model and both yield rotationally cold DCl products with little energy in the alkyl fragments. Despite these similarities, we measure DCl(upsilon' = 0,J' = 1) product polarizations that differ greatly for these two reactions. For the Cl + CD4 reaction, we find that J(DCl) is maximally aligned perpendicular to an axis close to the product scattering direction, u(DCl). For the Cl + C2D6 reaction, we find that J(DCl) is half-maximally aligned perpendicular to the line-of-centers direction. We interpret these results in terms of the location of the D-atom transfer along the reaction coordinate, positing that the D-atom transfer for the Cl + CD4 reaction occurs late in the reactive process and the D-atom transfer for the Cl + C2D6 reaction occurs earlier near the distance of closest approach. We interpret the difference in the locations of the D-atom transfer to be the cause of the large differences in the Arrhenius pre-exponential factors of the Cl + CD4 and Cl + C2D6 reactions. (C) 1997 American Institute of Physics.