The Application of the Three Dimensional Patterson Method and the Crystal Structures of Proustite, Ag₃AsS₃, and Pyrargyrite, Ag₃SbS₃

It is shown that the three dimensional Patterson method can be so simplified by the use of the symmetry properties of the crystal under consideration that its use in determining the positions of atoms in crystals is practicable. This method is then used to determine the positions of the heavy atoms in proustite, Ag3AsS3. The positions of the sulfur atoms are found by the use of the covalent atomic radii and assumptions concerning bond directions. The structure so derived is found to be compatible with the observed data. Proustite is found to contain pyramidal AsS3 groups and silver atoms forming two bonds to sulfur in almost opposed directions. Pyrargyrite, Ag3SbS3, is found to have almost the same structure as proustite. The analytical statement of the structures is as follows:-- The space group C63v - R3c, is common to both proustite and pyrargyrite. The special positions of C63v are (in hexagonal axes) 2a) 0,0,z; 0,0,½+z 6b) x,y,z; y,x-y,z; y-x,x,z; y,x,½+z; x,x-y,½+z; y-x,y,½+z; and positions derived from these by the operations of the rhombohedral lattice. The parameter values are:-- Proustite ao = 10.74 Å, co = 8.64 Å 2As in 2a) ZAs = 0.000 6Ag in 6B) xAg = 0.246 yAg = 0.298 zAg = 0.235 6S in 6b) xS = 0.220 yS = 0.095 zS = 0.385 Pyrargyrite ao = 11.04 Å, co = 8.71 Å 2Sb in 2a) ZSb = 0.000 6Ag in 6B) xAg = 0.250 yAg = 0.305 zAg = 0.210 xS = 0.220 yS = 0.105 zS = 0.355