A re-investigation of the crystal structure of quadratite, ideally AgCdAsS3, was undertaken using a single crystal from the type locality, Lengenbach, Binntal, Switzerland. The average of five electron microprobe analyses led to the empirical formula (Ag0.994Cd0.738Pb0.231Cu0.006Tl0.005Mn0.003Fe0.004Zn0.002 Cr0.001)Σ=1.984(As0.955Sb0.003)Σ=0.958S3.058. A single-crystal structure refinement (R1 = 4.84% for 558 observed reflections) shows that quadratite crystallizes in the space group P4322 and exhibits an atomic arrangement similar to that of the recently approved new mineral manganoquadratite, AgMnAsS3. Like manganoquadratite, quadratite adopts a galena-derivative framework, with metal atoms occupying all the available octahedral interstices, although only M1 and M2 cations, occupied mainly by Cd, adopt a fairly regular octahedral coordination; the M3 cation, occupied by Ag, is located outside the center cavity in a square-pyramidal coordination, whereas Pb at the split position M3′ coordinates six S atoms. Arsenic also adopts a 3 + 3 asymmetrical coordination, thus forming the AsS3 pyramidal groups that typically occur in sulfosalts.
The structure can be also described as a stacking of BAB slabs [A: (Cd,Ag)CdS2 atomic plane; B: (Ag,Pb)AsS2 atomic plane] along [001]. The rectangular unit cell of these slabs is oriented diagonally to the a axes of quadratite and consecutive slabs are related via interlayer twofold rotation operations parallel either to [100] or to [010]. This ambiguity leads to an OD structure with various possible stacking sequences, from which the tetragonal space group P4322 was observed.