Tetrahedrite is the most common of the sulfosalt minerals and is one of the primary sources of silver in the world today. Although relatively simple structurally, the compositional complexity has hindered systematic investigations. Accordingly, three separate, but related, investigations were undertaken to address this problem.

In the first investigation, available compositional data for 1271 samples of natural tetrahedrite and 295 of synthetic tetrahedrite were examined. They show: compositional ranges of four to ten Cu, zero to six Ag, and a total of two (Fe,Zn,Hg) atoms, complete substitution (up to four atoms) among As, Sb and Te, and a total of 13 atoms of S per formula unit. Data on contents of Pb, Bi and Cd in natural samples are insufficient to define their compositional ranges, and virtually no data exist on other substitutions, involving Co, Ni, Mn and Au. For the purposes of explaining compositional variations in tetrahedrite, the simple Brillouin-zone model of bonding (Johnson & Jeanloz 1983) is superior to any ionic model.

Next, linear regression analyses of the data gathered defined equations that predict the cell dimension of natural and synthetic tetrahedrite in terms of atoms per formula unit to within an average of ± 0.02 Å. Variation of the Fe/Zn ratio has no appreciable effect on a. Calculation of changes of molar volume with composition indicate that As:Sb, Bi:Sb, Cu:(Fe,Zn), Hg:(Fe,Zn) and Cd: (Fe,Zn) substitutions may be ideal or nearly so, whereas Ag:Cu substitution is not.

The crystal chemistry of tetrahedrite can be rationalized by considering the structure to be generally analogous to sodalite, i.e., a framework of comer-connected M(l)Y4 tetrahedra containing an ZM(2)₆ octahedron rather than an interframework cation or anion. Framework rotation (¢) is increased by increases in the M(1)—Y and X—Y bond lengths, but decreased by increases in the M(2)—Y bond length. Distortion of framework tetrahcdra is negligibly affected by the M(1)—Y bond length and greatly affected by the X—Y bond length. Increases in the M(2)—Y bond length cause the distortion to decrease, then increase, creating a state of no distortion to the framework polyhedra at a bond length of 2.36 Å and a ¢ of 48.4°.

Although not explicitly demonstrated, the possibility exists that ordering of the divalent cations in the tetrahedrite framework may occur. Such ordering would explain the lirr1it of divalent cations normally observed in tetrahedrite and would reduce the symmetry of the structure.