ORE GEOLOGY1.Phase Equilibria In Ore-Bearing Systems

 aim 
to simulate the natural ore-forming environments in the laboratory.
Problems
‘plague of metastability’
(a) crystal-chemical complexities
extensive substitution (single, coupled, multilateral)+ dominantly covalent (and metallic) bonding => extremely distorted coordination polyhedra and close metal-metal distances in many structures promote non-stoichiometry, charge imbalance and wide solid solution range

(b) faster reaction kinetics and consequent non-quenchability
Phases such as sphalerite, arsenopyrite, tetrahedrite,
pyrite, hematite, magnetite, wolframite have lower metallic characteristics (lowest degree of metallic bonding expressed as low frequency of short M1-M2 bonds) are most useful
On the contrary, Cu-Fe-sulfides and Cu-sulfides take little time to
reequilibrate  Hence, barring the above refractory minerals, laboratory based
phase equilibrium studies have very little application as far as extrapolation to natural ores is concerned.

(c) dominant control of fS2 on phase assemblages
Standard state of sulfur
The standard state of sulfur is conveniently chosen as ideal diatomic sulfur gas, S2, at one bar fugacity and the temperature of interest. This state is used in spite of the fact that the same is not physically attainable due to condensation of solid or liquid sulfur below 614°C. Therefore fS2 is numerically equal to PS2 (and aS2) in atmosphere. The choice of this standard state is dictated because otherwise the sulfidation curves will otherwise bend at the melting, transition and boiling point of the yellow colored orthorhombic sulfur, stable at the normal P-T condition.
Parameters
P,T,X,fugacity,activity
Representation with the help of different diagrams
P-T,
T-X,
T-f(S2),
T-f(O2),
f(S2)-f(O2).
BASIC IDEAS USED
Application of laboratory data to natural assemblages
for quantitative interpretation in the form of phase diagrams requires recognition of
independent variables. The way to achieve this goal is through the Gibbs phase rule, a
fundamental statement in chemical thermodynamics, relating the number of stable phases
(p) in an equilibrating assemblages, to the number of independent components (C) and
the number of independent degrees of freedom (f).
Derivation: 
 If we represent the composition of all the phases in terms of Xi (X1, X2, X3...
etc), then there will be an Xi term of every component in every phase. Hence for ‘p’
phases there will be ‘cp’ compositional variables. In general, there will be two additional physical variables (P and T). Hence the total number of variables (unknowns) = cp + 2.
Since the sum of Xi in each phase = 1.0, then for ‘p’ phases, there will be p-number of c equations like ∑ X i = 1 .
Transfer of chemical components takes place in the decreasing direction of chemical potential (μi), implying that at equilibrium, μI of each component is the same in every phase where it appears. Hence for component ‘i’
μ iα = μ iβ = ............μ ip
(1)
For p-1 pairs, there will be c(p-1) number of the above equations making the total number
of equations = p+ c(p-1).
Now from the simple principle of linear algebra, the variance of the system of equations
= number of variables – number of equations
Hence f = cp + 2 - p-cp + c
f=c–p+2
It must be noted that the above phase rule is predicted at equilibrium with uniform P, T and μI throughout and that the identity of each variable is lost in the process of account, which can not be recovered by manipulation of the equations.
Theoretically such diagrams are polybaric, but
because most solids and liquids are relatively incompressible, the P variation has little
effect on phase relation and the phase rule becomes f = c –p +1.
P – T diagram
These diagrams are drawn on the basis of Clausius- Clapeyron’s eqn. Given by
dP/dT= ΔS/ΔV=ΔH/TΔV
derived from dG = ΔVdP – ΔSdT = 0 and ΔG = ΔH – TΔS = 0.
fS2 – T diagrams2MxSy + S2 = 2MxSy+1
ΔG° = –RTln K = RTln fS2 = 2.303RT log fS2
ΔH° – TΔS° = 2.303RT log fS2
log fS2 =ΔH0/2.303RT - ΔS0/2.303R
differntiating above eqn we can plot the diagram.
fS2–fO2 diagrams
Fe3O4 + 3S2 = 3FeS2 + 2O2
2Fe2O3 + 4S2 = 4FeS2 + 3O2
K can be calculated from these eqns and used in eqn below
ΔG o = − RT ln K − ( P − 1) ΔVS


Eh-pH diagrams
Eh = E° +0.059(log K)/n



DIFFERENT SYSTEMS:
 

The Fe-S system
This is one of the most studied sulfide system, both in mineralogy and metallurgy. Pyrite and pyrrhotite are the only two sulfide minerals to be called rock-forming minerals.
The Fe-S system is also an important bounding binary in many multi-component systems such as Fe-Zn-S, Fe—Ni-S, Cu-Fe-S, Fe-As-S, Cu-Fe-Zn-S etc.).
The phase relation above 400°C is clear and straight forward The central portion of the system is dominated by the large, high- temperature pyrrhotite solid solution field constitutes extreme solid solution from stoichiometric FeS toward more S- rich compositions. This high-T form with hexagonal NiAs-type structure accommodates solid solution by random vacancies on the Fe sites within the lattice. Hence, the composition of high temperature pyrrhotites, except for FeS, is best given as Fe1-XS. The maximum thermal stability of the pyrrhotite solid solution at pressure = 1 bar is 1192°C, above which it melts incongruently. The eutectic between pyrrhotite and Fe is at 988°C, 56% Fe. Brett and Bell (1969) found that the eutectic temperature is P-insensitive up to 30 kbar but then rises rapidly, reaching 1160°C at 100 kbar.
 S-poor portionunimportant for
terrestrial ore forming processes, do apply directly to lunar and meteoritic samples and iron smelting
On the S-rich portion
the minimum temperature of existence of a sulfide liquid is 1088°C; above this temperature, there is a broad field of
liquid immiscibility comprising of a sulfide-rich and a sulfur-rich liquids.
 
The common occurrence of pyrite + pyrrhotite along with temperature dependence of pyrrhotite composition in the above assemblage, led Arnold (1962) to propose the pyrrhotite geothermometers.
utility of the pyrrhotite thermometry is only restricted
to samples where rapid equilibration between pyrite and pyrrhotites (eg. in basalts) takes place.
Otherwise, during slow cooling, the pyrrhotite composition slides down the solvus to a more Fe-rich composition.
A further complication in most ore deposits is the inversion to monoclinic pyrrhotite either by cooling below 254°C or as a low-temperature oxidation product.
X FeS in Po= n FeS/(n FeS + n S 2)
using the Gibbs-Duhem equation for the FeS-S2
binary, which can be written as
XS2 dlogfS2 + XFeS dlogaFeS = 0from this aFeS can be calculated.



The Fe-Zn-S SystemIn addition to phases encountered in the Fe-S systems, only new phases that appear in this ternary are sphalerite and wurtzite polytypes.
Sphalerite has a cubic closed packed (ccp) structure in which every alternate tetrahedral site is empty. Iron, along with Mn and Cd enters the structure by substituting for Zn and results in an increase in cell volume. Because of its refractory nature and wide variation in Fe content, sphalerite has been tried as a geochemical sensor for ore forming environment.
At 742°C, in the T - X section of Zn-Fe-S system,
pyrite incongruently breaks down to Po + S- rich liquid
From this Point (I), three invariant curves emanate:
(1) Sp + Po + S
(2) Sp + Py + Po
(3) Sp + Py + S

Sp + Py + HPo solvus remains vertical below 550°C at 20.7 ± 0.6 mole % FeS. Hence, for the major portion of geological temperature range this assemblage can not be used as a geothermometer.

Sp Geobarrometer : sphalerite composition in the assemblage Sph + Py + Hpo furnishes excellent pressure values that compare reasonably well with those estimated from silicate barometers.

VFeS is large, compared to VZnS --increase in cell edge of sphalerite with Fe content .
In a system where aFeS is buffered by Py + Hpo, sphalerite should become less Fe-rich with increasing pressure.
this geobarometer is T-independent within much of the
geologically important P-T ranges.
It is important to note that such T- insensitiveness increases with increasing pressure implying that sphalerite barometry is works better in situations when the ore are metamorphosed to relatively higher grades (P ≥5 kbar).
  
for successful application of this barometer certain prerequisites
1) coexistence of sphalerite with both the Fe-sulfides(Po,Py) to
ensure the aFeS- buffered condition
2)Additionally, sphalerite should be analyzed in grains without any chalcopyrite or pyrrhotite blebs in order to make certain preservation of its pristine P-dependent composition.

Assemblage Sp + Py
 fS2 – T relationship can be calculated using
FeS (in Sp) + 0.5 S2 = FeS2
considering a value of 2.3 for γ FeS
log X FeS in Sp = 6.65 –7340/T – 1/2 log fS2

Assemblage Sp + Tr + Fe
applications are only limited to meteorites
Sphalerite composition, buffered by troilite (Tr) and Fe (2Fe + S2 = 2FeS)
fixes aFeS at unity for all temperature. The effect of pressure on Sp + Tr solves is large,
The thermodynamic deduction is given below
X FeS in Sp= a FeS / γ FeS
differentiating this wrt P,
(XFeS)P2−(XFeS)P1 in Sp=−[(VolumeSp−VolumeTr)(XFeS)](P2− P1)/RT

 The Cu-Fe-S system
The phases occurring in the system Cu-Fe-S are found in many geological environments and in lunar and meteoritic materials.
Phase relation is not properly understood due to, large number of phases, extensive solid solution, non-stoichiometry, non-quenchability and metastability.
Phase equilibria at 400°C and above are dominated by three solid solutions (1) chalcocite - digenite - bornite
(2) (Iss)
(3) pyrrhotite solid solution

absence of complete solid solution between Cc-Di-Bn and the Iss, in spite of their similarity of structure and cell size,suggests differences in the type of bonding.
The Iss has a cell edge of 5.4Å, sphalerite-type, fcc unit cell  and
chalcopyrite cell is same excepting doubling in the C-axis direction.

1)On cooling below 557°C,
chalcopyrite appears as an ordered (tetragonal) phase.
Above this temp -transforms to a cubic Iss phase (and small amount of pyrite).
2)The orthorhombic polymorph of cubanite (CuFe2S3) is only stable up to ≈210°C  above which it inverts to cubic Iss.
3)Natural intergrowths of chalcopyrite-bornite, chalcopyrite-cubanite;
and talnakhite (Cu9Fe8S16), mooihoekite (Cu9Fe9S16) and haycockite (Cu4Fe5S8) are likely formed as decomposition products of initially deposited high temperature Iss.


The Fe–Ni–S system
1)Ni-bearing magmatic ore deposits formed by liquid immiscibility. 2)pentlandite,(Ni,Fe)9S8 occurs in some hydrothermal ore associations.


At 1000°C, the Fe–Ni–S system is dominated by
1)a large liquid field
2)a solid solution field extending from pyrrhotite (Fe1-xS) towards nickel monosulfide (Ni1-xS).

At temperatures <992°C, the monosulfide solid solution (mss) becomes complete and dominate the central portion of the system

At 650°C,  the mss coexists
with (Fe,Ni)S2 or (Ni,Fe)S2 on the S-rich side
or
(Ni,Fe)3±xS2 or γ– or α–(Fe,Ni)on the metal rich side.

On further cooling, the mss field narrows down

below 610°C
pentlandite appears on the metal rich side
violarite on the S-rich side.

Pentlandite is therefore entirely a subsolidus phase, formed by exsolution of the mss.

at 400°C
disulfides (Ni7S6 and Ni3S2), that have limited solid solubility with various (Ni,Fe) alloys

below 300°C
The mss begins to unmix

Below 212°± 13°C,
the pentlandite-pyrite tie line is established.

near 200°C
mss is shown breaking into three segments.

at 25°C from the study of natural assemblages.
Although the pentlandite-violarite natural assemblage is observed, it is generally metastable. Hence, the preferred tie lines are shown by joining millerite with pentlandite and pyrite.

At 600°C temperature,
diffusion rates will be too high but
the driving force for nucleation that depends on the degree of undercooling below the solvus will be small
Slow cooling
Fast diffusion +heterogeneous nucleation will lead to the formation
of granular pentlandite. 
rapid cooling
 a greater degree of undercooling is necessary to cause unmixing. Here,
homogeneous nucleation may lead to oriented flames.

Fe-As-S System
only one ternary phase, arsenopyrite, FeAsS.
Important factors to study :

* compositional variation of arsenopyrite in terms of
 As/S ratio on the FeS2 (pyrite) –FeAs2 (löllingite) join, and
  its dependence on formation (or equilibration) temperatures.

In the high temperature portion,
arsenopyrite coexists with pyrrhotite, löllingite, As, or an (As,S) liquid in assemblage 1 through 4.

Between 491° and 363°C,
arsenopyrite can coexist with pyrite, pyrrhotite, löllingite, As, or (As,S) liquid in the assemblages 5 through 8.

**
Since arsenopyrite composition is a function of both temperature and fS2, the same can be used a geothermometer, if arsenopyrite occurs in an fS2- buffered assemblage.(On the other hand, ƒS2 – unbuffered assemblages
furnish a range in T and fS2)
The common ƒS2 – buffered univariant assemblages include
Asp + Lo + Po,
Asp + Py + Po,
Asp + Py + As,
in which atomic %As in arsenopyrite uniquely fix both T and fS2


The Fe – Zn – As – S system
Thermobarometric interpretation of sulfide ores is hampered by problems of mineral reequilibration. However, this problem can be minimized by making use of refractory ore minerals that offer best candidates for preserving their composition pertaining to ore forming environments.
The Fe-Zn-As-S system is potentially one of the most useful
systems for thermobarometric interpretations because it involves three of the most common and refractory sulfide minerals, namely
1)pyrite,
2)sphalerite
3)arsenopyrite

# From Arsenopyrite composition- both fS2 and T can be evaluated.
#Sp barometry can be pursued as Sp composition is unaffected by Arsenic.


The Cu – Fe – Zn – S system
more common in hydrothermal ore deposits than those in the arsenide- bearing system but,
in contrast,
commonly undergo post-depositional reequilibration.Not only the Cu- and Cu-Fe-sulfides readjust their composition during cooling, presence of minerals such as chalcopyrite promotes changes in the otherwise refractory sphalerite.
chalcopyrite disease :
(A very common feature in Zn- and Cu-bearing hydrothermal veins, volcanogenic, and metamorphosed massive sulfide deposits is the texture of dispersed blebs and rods of chalcopyrite in sphalerite)

[This texture has been notionally thought to be an exsolution product.
But experimental studies oppose this thought.
1)up to 500°C, solubility of chalcopyrite in sphalerite is negligible.
2)natural sphalerites containing chalcopyrite disease occur in ores such as carbonate- hosted Pb-Zn ores (100°–150°C) and unmetamorphosed VMS ores (200°–300°C)]

Explaining Cp Disease  in Sp:
(i) epitaxial growth during formation of sphalerite or
(ii) selective replacement of Fe- rich zones in sphalerite by a Cu-bearing chloride fluid,

Sphalerite stars or crosses,:
interpreted to have been formed due to exsolution,
because of appreciable solubility of ZnS in CuFeS2.