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

Citation

Harker, David (1936) The Application of the Three Dimensional Patterson Method and the Crystal Structures of Proustite, Ag₃AsS₃, and Pyrargyrite, Ag₃SbS₃. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7x7x-cv79. https://resolver.caltech.edu/CaltechTHESIS:03312025-223924929

Abstract

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 C⁶_3v - R3c, is common to both proustite and pyrargyrite. The special positions of C⁶_3v 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

a_o = 10.74 Å, c_o = 8.64 Å

2As in 2a) Z_As = 0.000

6Ag in 6B) x_Ag = 0.246

y_Ag = 0.298

z_Ag = 0.235

6S in 6b) x_S = 0.220

y_S = 0.095

z_S = 0.385

Pyrargyrite

a_o = 11.04 Å, c_o = 8.71 Å

2Sb in 2a) Z_Sb = 0.000

6Ag in 6B) x_Ag = 0.250

y_Ag = 0.305

z_Ag = 0.210

x_S = 0.220

y_S = 0.105

z_S = 0.355

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