Computer Modelling of the Dolomite Structure Using a Mean Field Approach

1. Introduction & Background

Dolomite is the mineral name for calcium magnesium carbonate, chemical formula CaMg(CO₃)₂, with the Ca and Mg ions on alternate sites in an ordered structure.

The ‘dolomite problem’ refers to the fact that for 200 years, scientists were unable to grow dolomite in the laboratory under the conditions believed to have formed it naturally. It occurs abundantly in geological deposits, and structures have been determined and published [1]. Computer modelling, using a mean field approach with the calcite structure as a starting point has been used to model the structure, motivated by a recent experimental paper which succeeded in synthesising dolomite [2]. These authors used a synthesis process involving removal of defects as the crystal grows, using ideas developed from atomistic simulations.

In this study we have modelled dolomite in two ways – (i) using a mean field approach with the calcite structure as a starting point and substituting Mg at the Ca site up to a 50:50 distribution, and (ii) using the experimental structure as a starting point [1].

2. Methodology

Calculations were performed using the GULP code [3], which uses interatomic potentials and lattice energy minimisation to model structures and properties. Full details are given in the subsections below.

2.1. Interatomic Potentials

The computer modelling work presented here was performed using interatomic potentials. The Buckingham potential has been employed, augmented with a term to represent the electrostatic interactions between ions, and it has the following form:

V (r) = A exp (-r/ρ) – Cr^-6 + q₁q₂/r

In the equation, A, ρ and C are parameters to be obtained by empirical fitting, and q₁, q₂ are charges on the interacting ions with ‘r’ being the interionic distance. The carbonate group is treated as a molecular ion, and three-body terms describe bond-bending about each O-C-O bond, and four-body torsional terms retain the planarity of the C0₃^2- group. The potential parameters used are given in section 3.1, and were taken from [4].

2.2. Lattice Energy Minimisation

Lattice energy minimisation can be used to calculate structures corresponding to a minimum in the lattice energy.

The total lattice energy E_latt is written as a sum of interactions between ions (described by interatomic potentials):

E_latt = ∑ V (r)

Then, by adjusting the structure (either the lattice parameters or atomic positions or both), the minimum energy structure is obtained. Note that a well derived potential would be expected to reproduce the structure without significant structural adjustment.

2.3. Mean Field Calculations

The dolomite structure has alternating Ca and Mg ions, and it has been modelled by the mean field method, in which the cation site is represented by an average of Ca and Mg in varying ratios (50:50 for dolomite). The advantage of this approach is that the calcite structure can be used as a starting structure, and any Ca-Mg structure of interest modelled. The disadvantage is that an averaged structure is being modelled, so specific Ca-Mg configurations are not considered by this method.

3. Results & Discussion

3.1. Mean Field Calculations

Starting with the calcite structure [1], Mg ions are successively substituted at the Ca site, and the structure was energy minimised at each point. This enables the structure corresponding to any concentration of dopant to be predicted, with dolomite corresponding to a 50% concentration. Potentials derived by Jackson and Price [5] were used, given in Table 1. Table 2 gives the calculated structures as a function of dopant concentration.

Charges (|e|): q(Ca) = 2.0, q(C) = 0 99805, q(O) = 0 99935

Bond bending constant k₃ = 9.3 179 eV rad^-2

Torsional constant k₄ = I.1392 eV

From Table 2, the predicted dolomite structure corresponds to 50% Mg concentration, and is compared with the experimental structure in Table 3.

From Table 3 it is seen that the ‘a’ and ‘b’ parameters agree with the Effenberger results to within 2.0%, and the ‘c’ parameter to within 4.0%. Considering that the starting structure was that of pure calcite, this is an encouraging result.

3.2. Lattice Energy Minimisation Calculations on the Experimental Structure

Finally, a lattice energy minimisation calculation was performed using the Althoff structure as a starting point. Results are given in Table 4, where it can be seen that similar agreement is obtained as with the mean field generated structure.