Institute of Geology and Dynamics of the Lithosphere at the University of Göttingen



International Conference on
Textures and Physical Properties of Rocks

October 13 (Wed) to 16 (Sat), 1999 in Göttingen, Germany

WORKSHOP 10:

Geoffrey E. Lloyd and Noel W. Thomas
(School of Earth Sciences, University of Leeds):

VORONOI POLYHEDRAL MODELLING: FROM CRYSTAL CHEMISTRY TO PETROPHYSICS



Mineral phase transformations and reactions occur throughout the crust and mantle as a response to changing pressure, temperature and composition (P, T, x) and are directly relevant to many geological and geophysical interpretations of Earth. Voronoi polyhedra constructed about each cation and anion site in the crystallographic unit cell fill all available space, leading to unique volumetric solutions and making quantitative geometrical modelling possible.

Use of Voronoi polyhedra to model phase transformations and reactions is based on:

1. variation in ionic polyhedral volumes and ratios;

2. interpretation of shared polyhedral faces;

3. polyhedral geometry.

The faces of Voronoi polyhedra correspond to pairwise interactions (i.e. ‘bonds’), from which face interaction indices can be defined, leading to the construction of phase structure maps. Alternatively, shared polyhedral vertices correspond to structural voids which are natural sampling points to probe clustering, introducing the concept of structural fingerprinting of phases.

As the characteristics of Voronoi polyhedra change with (P, T, x), it is possible to simulate geometrically the effect of one variable on the others using experimentally constrained data. Such changes can be used to model the behaviour of minerals in terms of their stability and/or tendency for transformation and/or reaction.

This Workshop will explain in detail, with on-site computer demonstrations, the Voronoi approach. We shall take for our main example the system olivine-spinel-perovskite, representative of a crust-to-lower mantle succession. However, we emphasise that the Voronoi approach is applicable to any mineral system, transformation and indeed metamorphic reaction. As such, we invite participants to bring their own P, T, x data (e.g. in the format required for use in SEM/EBSD computer identification programs).

Figure 1. Voronoi polyhedra constructed about individual ions, showing the various paramaters available to quantify crystal chemical modelling of mineral phase transformations and metamorphic reactions.

Figure 2. Examples of Voronoi polyhedra for magnesium silicate perovskite. The simple polyhedra (i.e. few faces) associated with Si ion suggests that this is structurally stable compared with the Mg and, especially, the O ions, which have more complex polyhedral shapes and volumes.

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Last updated: May 19, 1999