Towards a model for the in situ origin of PGE reefs in layered intrusions: insights from chromitite seams of the Rum Eastern Layered Intrusion, Scotland

Abstract

The current debate on the origin of platinum-group element (PGE) reefs in layered intrusions centres mostly on gravity settling of sulphide liquid from overlying magma versus its introduction with interstitial melt/fluids migrating upward from the underlying cumulate pile. Here, we show that PGE-rich chromitite seams of the Rum Eastern Layered Intrusion provide evidence for an alternative origin of such deposits in layered intrusions. These laterally extensive 2-mm-thick chromitite seams occur at the bases of several cyclic mafic–ultramafic units and show lithological and textural relationships suggesting in situ growth directly at a crystal–liquid interface. This follows from chromitite development along the edges of steeply inclined culminations and depressions at unit boundaries, even where these are vertically oriented or overhanging. High concentrations of PGE (up to 2–3 ppm Pd + Pt) are controlled by fine-grained base-metal sulphides, which are closely associated with chromitite seams. The following sequence of events explains the origin of the PGE-rich chromitite seams: (a) emplacement of picritic magma that caused thermal and mechanical erosion of underlying cumulate, followed by in situ growth of chromite against the base, (b) precipitation of sulphide droplets on chromite grains acting as favourable substrate or catalyst for sulphide nucleation, (c) the scavenging of PGE by sulphide droplets from fresh magma continuously brought towards the base by convection. Since the rate of magma convection is 10⁵–10⁷ times higher than that of the solidification (km/year to km/day versus 0.5–1.0 cm/year), the in situ formed sulphide droplets can equilibrate with picritic magma of thousands to million times their own volume. As a result, the sulphide-bearing rocks are able to reach economic concentrations of PGE (several ppm). We tentatively suggest that the basic principles of our model may be used to explain the origin of PGE-rich chromitites and classical PGE reefs in other layered mafic–ultramafic intrusions.

Appendix 1: Derivation of an equation governing mass transfer

The redistribution of impurities in melt as a function of distance from a solid–liquid interface during the solidification of metal alloys is analysed mathematically in several publications (Tiller et al. 1953; Smith et al. 1955; Lasaga 1982). According to these studies, the steady-state distribution of impurity in the melt is governed by the following differential equation

$$D\frac{{{\text{d}}^{2} C_{L} }}{{{\text{d}}x^{2} }} + V\frac{{{\text{d}}C_{L} }}{{{\text{d}}x}} = 0 $$

(2)

where C _L is the concentration of impurity in the melt, D is the coefficient of diffusion of the impurity in the melt, V is the velocity of the interface (assumed to be constant) and x is the distance measured from the interface into the liquid.

The problem is closed using the following boundary conditions:

$$C_{L} = C_{0} \quad {\text{at}}\quad x = \infty $$

(3)

$$- D\frac{{{\text{d}}C_{L} }}{{{\text{d}}x}} - VC_{L} = - VKC_{L} \quad {\text{at}}\quad x = 0 $$

(4)

where C ₀—the initial concentration of impurity in the melt, K—partition coefficient of impurity between solid and melt. The condition (3) is based on two assumptions: (a) the mass of melt significantly predominates over that of the solid so that one can neglect any changes in impurity concentration at an infinite distance from the interface, (b) mass transfer in the melt occurs only by diffusion, which allows us to describe the concentration of impurity in the melt using an Eq. (2) on the entire interval of the melt from a growing solid to infinity. Condition (4) enforces the conservation of matter across the crystallisation front.

Direct application of equations derived by Tiller et al. (1953) and Smith et al. (1955) to real situations is limited, however, because of convective mixing in melt (e.g. Bacon 1989). The influence of convection can be taken into account by assuming that a mass transfer within the liquid boundary layer occurs by diffusion, whereas in the main volume outside of this layer, it takes place by convection (see Fig. 6). With a large volume of melt and intensive convection, the concentration of impurity outside the liquid boundary layer can be considered constant. In this case, the boundary condition (3) can be re-written as

$$C_{L} = C_{0} \quad {\text{at}}\quad x = \delta $$

(5)

where δ—thickness of boundary layer. Solving of the differential Eq. (2) with the boundary conditions (5) and (4) gives

$$C_{L} = C_{0} \frac{{\exp \left[ {\frac{V}{D}\left( {\delta - x} \right)} \right]\left\{ {1 + K\left( {\exp \left[ {\frac{V}{D}x} \right] - 1} \right)} \right\}}}{{1 + K\left( {\exp \left[ {\frac{V}{D}\delta } \right] - 1} \right)}} $$

(6)

Then, the concentration of impurity in the crystallizing material (C _S ) will be defined as

$$C_{S} = K\left. {C_{L} } \right|_{x = 0} = C_{0} \frac{KY}{{1 + K\left( {Y - 1} \right)}};\, Y= \exp \left[ {\frac{V}{D}\delta } \right] $$

(7)

However, Eqs. (6) and (7) describe the concentration of impurity in the melt and in the solid in a steady state, that is at $t \to \infty$, where t is the time from the onset of crystallisation. Under steady-state conditions, the amount of impurity consumed at the solid–liquid interface is balanced by the amount that diffuses towards this interface. In order to determine the time t at which the process can be considered to be at steady state, we have done a series of numerical experiments. Mass transfer in the system with the solid–liquid interface moving with the constant rate (V) can be described by the differential equation

$$D\frac{{\partial^{2} C_{LT} }}{{\partial x^{2} }} + V\frac{{\partial C_{LT} }}{\partial x} = \frac{{\partial C_{LT} }}{\partial t} $$

(8)

with the boundary conditions in the liquid boundary layer approximation

$$C_{LT} = C_{0} \quad {\text{at}}\quad x = \delta \quad {\text{for}}\,{\text{all}}\,t $$

(9)

$$D\frac{{{\text{d}}C_{LT} }}{{{\text{d}}x}} + V(1 - K)C_{LT} = 0\quad {\text{at}}\quad x = 0\quad {\text{for}}\,{\text{all}}\,t $$

(10)

and initial condition

$$C_{LT} = C_{0} \quad {\text{at}}\quad t = 0\quad {\text{for}}\,{\text{all}}\,x > 0 $$

(11)

This equation was solved numerically. The condition at which the system reaches the steady state was taken as

$$\left| {\frac{{C_{S} - K\left. {C_{LT} } \right|_{x = 0} }}{{C_{S} }}} \right| < 0.0001 $$

(12)

where C _S is given by Eq. (7), and C _LT is determined by solving the differential Eq. (8) with the conditions (9–11).

The model parameters for the case of silicate melt from which PGE is scavenged by an in situ growing sulphide-bearing chromitite seam were taken to vary in the following ranges: D = 10⁻⁶–10⁻⁷ cm²/s, V = 30–300 μm/day, δ = 100–500 μm, K = 500 (choice of parameters is justified in the main text). Some variants of the numerical solution of Eq. (8) with conditions (9–11) for different values of parameters are shown in Fig. 11. In all models, the thickness of a solid layer of chromitite seam grown before the system has reached a steady state was less than 70 μm. This constitutes less than 3.5 % of an average thickness (2 mm) of chromitite seams in the Rum Complex. It can therefore be argued that the chromitite seams would essentially form under conditions of steady-state diffusion across a compositional boundary layer. This allows the use of Eq. (7) to calculate the PGE content in the chromitite seams.

Fig. 11

PGE concentrations within compositional boundary layer adjacent to an in situ growing sulphide-bearing chromitite seam taken at different time intervals from the beginning of crystallisation and at different values of parameters involved. In all models, the initial concentration of PGE (C ₀) in the melt is taken as 15 ppb, the bulk partition coefficient (K) of PGE between solid and melt is taken as 500. a Time to attain steady state is 726 s; during this time, the thickness of the solid layer attains 0.84 μm; b time to attain steady state is 19,900 s; during this time, the thickness of the solid layer attains 70 μm. A black dotted line corresponds to steady state that is defined by Eq. (6)