578 MINERALS/Sulphides slight nonstoichiometry (e.g galena (PbS) shows ptype conductivity in lead-deficient samples and n-type conductivity in sulphur-deficient samples) Given that the great majority of sulphide minerals are opaque, the optical properties of interest are those observed in reflected light from polished sections The qualitative optical properties commonly serve for routine identification, but definitive characterization can be greatly aided by measuring reflectance at set wavelengths, or a whole series of wavelengths, across the visible-light region Sulphide Mineral Stability Much work has been done to establish the stability relations of sulphide minerals in terms of variables that include temperature, pressure, composition, and the activities of various components The Fe–S system is the most important binary sulphide system because the iron sulphides are, by far, the dominant sulphide minerals in terms of geological abundance and variety of geological occurrences Furthermore, the Fe–S system is an integral part of other important more complex systems such as the Fe–Zn–S, Cu–Fe–S, and Fe–Ni–S systems The phase relations in the condensed Fe–S system above 400 C (Figure 3A) have been the subject of numerous studies and, in contrast to the low-temperature relationships, are well understood The central part of the system is dominated by the large high-temperature pyrrhotite field of solid solution from stoichiometric FeS towards more sulphur-rich compositions This high-temperature form with a hexagonal NiAs-type structure accommodates solid solution by random vacancies at the iron sites within the lattice Hence, the compositions of high-temperature pyrrhotites, except for pure FeS, are best given as Fe1 xS, where x is to $0.14 The maximum thermal stability of the pyrrhotite solid solution at pressures below about atmosphere is 1192 C, above which it melts congruently Pyrite has, at low pressures, a maximum thermal stability of 742 Æ 1 C The upper thermal stability of pyrite rises by approximately 14 C per kilobar of confining pressure In spite of numerous studies, the phase relations in the Fe–S system at temperatures below 350 C are incompletely understood A temperature–composition diagram for the system between FeS and FeS2 from 0 C to 350 C is shown in Figure 3B Phase relations in the compositional regions Fe–FeS and FeS2–S remain straightforward, essentially as shown in Figure 3A, but the central part of the system is exceedingly complex This complexity is caused by the crystal chemistry of the pyrrhotites, as discussed above, where iron atoms can be omitted, leaving holes or vacancies At low temperatures, ordering of vacancies occurs, resulting in the development of various superstructures The best-known of these superstructures is that of monoclinic pyrrhotite (Fe7S8) In this case, the vacancies occur in alternate layers of iron atoms parallel to the basal plane and in alternate rows in those layers (Figure 2C) This is known as the 4C structure, because the superstructure has a unit cell that is four times the c dimension of the parent nickel arsenide-type cell Although the structure of monoclinic pyrrhotite is well established, the structures of those compositions lying between FeS and Fe7S8 remain uncertain Numerous superstructure types have been reported for these intermediate pyrrhotites, including examples with nonintegral multiples of the parent-cell c and a dimensions (so-called NC and NA types) Many reported superstructures have not been observed in natural samples, where there is evidence of compositions clustering around Fe11S12, Fe10S11, and Fe9S10, as well as Fe7S8 These compositions also correspond to superstructures with high degrees of order, the 5C (Fe9S10) and 6C (Fe11S12) superstructures The thermodynamic stability of the various pyrrhotites, particularly the intermediate pyrrhotites, is problematic, with kinetic controls exerting the major influence over the compositions and structure types observed The highly ordered monoclinic pyrrhotite (Fe7S8) and troilite (FeS, a 2C superstructure produced by distortion of the nickel arsenide hightemperature form) may be stable phases in the system, but reported or measured free-energy minima suggest that only pyrite and troilite are truly stable phases Much sulphide is formed in sedimentary or hydrothermal environments, so phase equilibria in aqueous systems are of particular interest The stability of pyrite, for example, has been considered as a function of many variables Perhaps the best-known relationships are those at 25 C, for which the stability of pyrite in aqueous solution has been examined as a function of the changing activities of two or more components in the system when the others are held constant Thus, for the system Fe–S–O–H, the activity of hydrogen ions (pH) has been plotted against the ‘activity of electrons’ (Eh), and either one or both of these variables have been plotted against the activity of sulphur (expressed as pS2 or pS2) Figure shows Eh–pH plots illustrating the stability of pyrite and other sulphides and oxides of iron in water at 25 C and atmosphere total pressure Figure 4A shows relationships at a total dissolved sulphur activity of 10 and illustrates the large stability field of pyrite under reducing conditions over a wide pH range By contrast, the stability field of pyrrhotite is extremely small Under more oxidizing conditions, haematite is the dominant iron mineral, with magnetite having